What is meant by statement "the one who sees Dhamma sees dependent origination"?

Dhamma in this clause is fourth Noble truth in meditating minds, the fold-eight-paths-noble-truth of the ordinary practitioner, lokiya-khandha. Because every end of each part of this sutta have the conclusion as 'you have to comprehend your meditation-minds as well, because your comprehending-minds are grasping-aggregates in paṭiccasamuppāda, too.Then you will giving up and getting rid of desire and greed for these five grasping aggregates is the cessation of suffering.'

The readers have to connect this sutta with KN paṭisambhidāmagga, especially bhaṅgañāṇaniddesa, because both place are the same sāriputta's teaching. You can see in the same chapter of the path of purification as well.

The introduction part of this sutta said "all skillful qualities-all kusala-dhamma":

“The footprints of all creatures that walk (such as paṭiccasamuppāda, catudhātu, ) can fit inside an elephant’s footprint, so an elephant’s footprint is said to be the biggest of them all.

“Seyyathāpi, āvuso, yāni kānici jaṅgalānaṃ pāṇānaṃ padajātāni sabbāni tāni hatthipade samodhānaṃ gacchanti, hatthipadaṃ tesaṃ aggamakkhāyati yadidaṃ mahantattena;

In the same way, ...all skillful qualities... can be included in the four noble truths.

evameva kho, āvuso, ...ye keci kusalā dhammā... sabbete catūsu ariyasaccesu saṅgahaṃ gacchanti.

And what you asking is answered already in the explanation of that introduction.

But the Buddha has said:

Vuttaṃ kho panetaṃ bhagavatā:

“One who sees dependent origination sees the teaching.

“yo paṭiccasamuppādaṃ passati so dhammaṃ passati;

One who sees the teaching sees dependent origination.”

yo dhammaṃ passati so paṭiccasamuppādaṃ passatī”ti.

And these five grasping aggregates are indeed dependently originated.

Paṭiccasamuppannā kho panime yadidaṃ pañcupādānakkhandhā.

The desire, clinging, attraction, and attachment for these five grasping aggregates is the origin of suffering.

And this part showing "all ..skillful qualities..." is the fold-eight-paths-noble-truth which enlightening the cessation-noble-truth:

Yo imesu pañcasu upādānakkhandhesu chando ālayo anunayo ajjhosānaṃ so dukkhasamudayo.

Giving up and getting rid of desire and greed for these five grasping aggregates is the cessation of suffering.’

Yo imesu pañcasu upādānakkhandhesu chandarāgavinayo chandarāgappahānaṃ, so dukkhanirodho’ti.

At this point, much has been done by that mendicant.

Ettāvatāpi kho, āvuso, bhikkhuno bahukataṃ hoti.

The long sutta often already included the answer, because "svākkhāto bhagavatā dhammo-buddha's teaching was the best teaching (because buddha [and his ariya students] connects these 4 subjects of genius [4 paṭisambhidā] together for each listener personally when he taught everything: causes & effects & linguistics of causes+effect & talents of these 4)".

So, when your question is appear almost at the end of Sutta Pitaka Vol 4 : Sutta. Ma. Mū. Mahāhatthipadopamasuttaṃ, you have to search for the answer at the previous paragraphs first. It is a proving tool you understand or not of each sutta, then you can search for the reference with the other sutta/part/nikāya/piṭaka. By this way, I can connects whole tipitaka together without conflicts.

Dhamma is the truthful recognition of things as they are. Form is not self. Consciousness is not self. Perception is not self. Feeling is not self. Volitional Formations are not self. Why are they not self ? Because they are impermanent. Why are they impermanent ? They are impermanent because they dependently arisen.When the dependent factors are removed the thing ceases to be.

Below I quote from SN 36.8 describe why 'feeling'(one of the five aggregates) is impermanent :

“Bhikkhus, while a bhikkhu dwells thus, mindful and clearly comprehending, diligent, ardent, and resolute, if there arises in him a pleasant feeling, he understands thus: ‘There has arisen in me a pleasant feeling. Now that is dependent, not independent. Dependent on what? Dependent on just this contact. But this contact is impermanent, conditioned, dependently arisen. So when the pleasant feeling has arisen in dependence on a contact that is impermanent, conditioned, dependently arisen, how could it be permanent?’ He dwells contemplating impermanence in contact and in pleasant feeling, he dwells contemplating vanishing, contemplating fading away, contemplating cessation, contemplating relinquishment. As he dwells thus, the underlying tendency to lust in regard to contact and in regard to pleasant feeling is abandoned by him.

Now that we understand Dhamma let us see what is dependent origination. Dependent origination is a theory which claims that All things are dependently arisen. The list of things it claims to have dependently arisen are longer. All those things are impermanent. In short ,Dependent origination shows the path impermanent phenomenon take to reach suffering. On this whole journey of dependent origination Self or I is not found at all.

Below I quote from SN 12.20 to support the claim that nowhere in dependent origination idea of self is found:

“When, bhikkhus, a noble disciple has clearly seen with correct wisdom as it really is this dependent origination and these dependently arisen phenomena, it is impossible that he will run back into the past, thinking: ‘Did I exist in the past? Did I not exist in the past? What was I in the past? How was I in the past? Having been what, what did I become in the past?’ Or that he will run forward into the future, thinking: ‘Will I exist in the future? Will I not exist in the future? What will I be in the future? How will I be in the future? Having been what, what will I become in the future?’ Or that he will now be inwardly confused about the present thus: ‘Do I exist? Do I not exist? What am I? How am I? This being—where has it come from, and where will it go?’

In both the cases we have reached the same conclusion that impermanent phenomenon means suffering which means they are not self. Therefore when one sees dependent origination one sees the Dhamma and vice versa.

Piya Tan's introduction to MN 28 says this:

The Mahā Hatthi,padopama Sutta contains an interesting statement attributed to the Buddha himself, but which is found nowhere else, namely, “He who sees dependent arising sees dharma; he who sees dharma sees dependent arising” ¹⁴ (paṭicca,samuppādaṁ passati, so dhammaṁ passati. Yo dhammaṁ passati, so paṭiccasamuppādaṁ passatî ti) [§28]. In fact, this quote is untraced in the Pali Canon as we have it and possibly belongs to some lost texts. The Sutta goes on to explain that the five aggregates of clinging arise interdependently (paṭicca,samuppannā). The Commentary explains the statement thus: “One who sees conditionality (paccaya) sees dependently arisen states (paticca,samuppanne dhamme); one who sees dependently arisen states see conditionality” (MA 2:230).¹⁵

Dependent arising is the most important epistemological model for explaining how our experiences arise through conditions and how they are interrelated to events and states around us. Dependent arising is the interrelatedness of dharmas, as Rupert Gethin points out:

To see dhammas is to see their interrelatedness; to see their interrelatedness is to see dhamma. One might rephrase the Nikāya saying, then, as: “He who sees dhammas sees dhamma; he who sees dhamma sees dhammas.” (Gethin 2001:151)

In his article “He who sees dhamma sees dhammas,” Gethin adds:

My suggestion is that this [MA 2:230 above] should be read in part as quite deliberate play on the meaning of dhamma, a play, moreover, that is entirely consonant with the Nikāyas. As we have seen, dhammas are mental and physical qualities, and seeing these dhammas as dhammas—seeing how they arise and disappear, seeing how they are dependently arisen—one sees the ultimate truth: he who sees dhammas sees dhamma. (Gethin 2004:536)

Gethin, however, is careful to add a caveat that he is not trying to impute any specific technical Abhidharma understanding to the Nikāyas, that he is not suggesting that dhamma is used in early Buddhist thought in the sense of an irreducible element. It is just that dhamma here is used in the general sense of a mental or physical quality.

Nevertheless, alongside the use of dhamma in the Nikāyas in the senses of the practices, truths and teachings that are recommended on the authority of the Buddha, there is a further usage already embedded in the Nikāyas: dhammas are the fundamental qualities, both mental and physical, that in some sense constitute—or better, support and maintain—experience or reality in its entirety. (Gethin 2004:536 f)

That the exact understanding and translation of dhamma in early Buddhist thought should remain elusive is understandable. The Dharma is “deep, hard to see, peaceful, sublime, beyond the sphere of reasoning [logic], subtle, to be known by the wise,”¹⁶ so that they are beyond bookish banter or academic pronouncements, but something to be personally and directly experienced leading to a wholesome life change. For this reason, even the Buddhas put the Dharma above themselves.¹⁷

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¹⁴ As will be explained below, it is important that “dharma” is here spelt in the lower case. Indeed, Pāli and other ancient Indian languages do not have capital letters, the use of which imposes a sense of permanence onto the idea that the word refers to—a notion foreign to early Buddhism.

¹⁵ Yo paṭicca,samuppādaṁ passatî ti yo paccaye passati; so dhammaṁ passatî ti so paṭicca,samuppanna,- dhamme passati. (MA 2:230)

¹⁶ Dhammo gambhīro duddaso duranubodho santo paṇīto atakkâvacaro nipuṇo paṇḍita,vedanīyo (M 1:167).

¹⁷ Dhammañ ñeva sakkatvā garuṁ katvā, Gārava S (S 6.2/1:138-140 = A 4.21/2:20 f) = SD 12.3.

I think Gethin's play on words is based on the fact that "dhamma" has several meanings.

Roughly, when he dhammas he means "things" (and the relationships between things), and when he say "dhamma" he means something like law-of-nature (as discovered by the Buddha) or "Buddhist doctrine" or "the teaching" -- so (my paraphrase), "he who sees things sees dependent arising in the relationships between things, and in that sees the important part of Buddhist doctrine."

Ven. Sujato also translates this as ...

One who sees dependent origination sees the teaching. One who sees the teaching sees dependent origination.

Sutta Central's dictionary alternatively translates passati as "sees; finds; understands".

Also maybe the "meaning" of the phrase is the sentences which follow it, if the phrase is understood as an introduction to those sentences and the sentences are understood as an explanation. The phrases which follow it are:

And these five grasping aggregates are indeed dependently originated. The desire, clinging, attraction, and attachment for these five grasping aggregates is the origin of suffering. Giving up and getting rid of desire and greed for these five grasping aggregates is the cessation of suffering.’

That's also the conclusion of the sutta and maybe the point of it.

"Dhamma" here should be written with a capital "D" and means the core teaching or core truth discovered and taught by the Buddha, namely, what is suffering and what is the cessation of suffering. Therefore, what is meant by statement “the one who sees Dhamma sees dependent origination” is one who sees dependent origination sees the Teaching/Truth of the Buddhas.

Bhikkhus, both formerly and now what I teach is suffering and the cessation of suffering.

MN 22

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Now it is for one who feels that I teach: ‘This is suffering,’ and ‘This is the origin of suffering,’ and ‘This is the cessation of suffering,’ and ‘This is the way leading to the cessation of suffering.’

AN 3.61

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Now this has been said by the Blessed One: “One who sees dependent origination sees the Dhamma; one who sees the Dhamma sees dependent origination.” And these five aggregates affected by clinging are dependently arisen. The desire, indulgence, inclination and holding based on these five aggregates affected by clinging is the origin of suffering. The removal of desire and lust, the abandonment of desire and lust for these five aggregates affected by clinging is the cessation of suffering.’

MN 28

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Enough, Vakkali! Why do you want to see this foul body? One who sees the Dhamma sees me; one who sees me sees the Dhamma. For in seeing the Dhamma, Vakkali, one sees me; and in seeing me, one sees the Dhamma.

What do you think, Vakkali, is form permanent or impermanent... suffering...not-self?”— “Impermanent... suffering... not-self, venerable sir.”…—“Therefore … Seeing thus … He understands: ‘… there is no more for this state of being.’”

SN 22.87

The word 'dhamma' can have various meanings, such as 'phenomena' (nature), law of nature (truth; law), duty according to law of nature (practise) and results of practise. In this case, it means 'Truth' or 'Law' (as 'Core Teaching/Doctrine'), as explained in SN 12.20.

“And what, bhikkhus, is dependent origination? ‘With birth as condition, aging-and-death comes to be’: whether there is an arising of Tathagatas or no arising of Tathagatas, that element still persists, the stableness of the Dhamma (dhammaṭṭhitatā), the fixed course/lawfulness of the Dhamma (dhammaniyāmatā), specific conditionality. A Tathagata awakens to this and breaks through to it. Having done so, he explains it, teaches it, proclaims it, establishes it, discloses it, analyses it, elucidates it. And he says: ‘See! With birth as condition, bhikkhus, aging-and-death.

SN 12.20

In SN 22.87, the Buddha told Vakkali:

“For a long time, venerable sir, I have wanted to come to see the Blessed One, but I haven’t been fit enough to do so.”

“Enough, Vakkali! Why do you want to see this foul body? One who sees the Dhamma sees me; one who sees me sees the Dhamma. For in seeing the Dhamma, Vakkali, one sees me; and in seeing me, one sees the Dhamma.

“What do you think, Vakkali, is form permanent or impermanent?”— “Impermanent, venerable sir.”…—“Therefore … Seeing thus … He understands: ‘… there is no more for this state of being.’”

Vakkali placed too much importance on directly seeing and experiencing the Buddha's physical form and presence, as he felt it is important and great. But the Buddha told him that the body is impermanent and there is nothing important and great about it. If you want to see and experience what is important and great about the Buddha, then understand the Dhamma (the Buddha's teachings) in detail.

Using the similar formula, the Buddha's words was relayed by Sariputta in MN 28:

"One who sees dependent origination sees the Dhamma; one who sees the Dhamma sees dependent origination."

So, what does that mean?

The Dhamma is so important and great. It is vast and deep. As stated in SN 6.1:

"This Dhamma (teachings or truth) that I have attained is deep, hard to see, hard to realize, peaceful, refined, beyond the scope of conjecture, subtle, to-be-experienced by the wise.

So, if the Dhamma (teachings) is so vast and deep, how can you learn all of it?

MN 28 provides the "shortcut". The formula "One who sees dependent origination sees the Dhamma; one who sees the Dhamma sees dependent origination," simply means that when you have thoroughly understood and "could see it through wisdom", then you have completely understood and realized the Dhamma. So, to understand the Dhamma completely, you need to thoroughly see and understand dependent origination through wisdom.

How can you see it through wisdom?

Khemaka explains in SN 22.89 that through the practice of Vipassana, one can see through wisdom:

"In the same way, friends, even though a noble disciple has abandoned the five lower fetters, he still has with regard to the five clinging-aggregates a lingering residual 'I am' conceit, an 'I am' desire, an 'I am' obsession. But at a later time he keeps focusing on the phenomena of arising & passing away with regard to the five clinging-aggregates: 'Such is form, such its origin, such its disappearance. Such is feeling... Such is perception... Such are fabrications... Such is consciousness, such its origin, such its disappearance.' As he keeps focusing on the arising & passing away of these five clinging-aggregates, the lingering residual 'I am' conceit, 'I am' desire, 'I am' obsession is fully obliterated."

So, basically, if you want to know what is important and great about the Buddha, learn the Dhamma. If the Dhamma seems too vast for you, remember that all you need to do is thoroughly understand dependent origination. But to thoroughly understand dependent origination, you need to see it through wisdom using Vipassana.

But to see through wisdom using Vipassana, there are some useful or helpful steps before that as found in AN 10.99, like practising virtues, sense restraint, mindfulness & alertness, abandoning hindrances etc.

This very question is exactly the topic of The Rice Seedling Sutra (Salistamba Sutra), one of the earliest known post-canonical sutras that can be classified as a missing link between Early Buddhism and Mahayana:

[...] Venerable Śāriputra then said to the bodhisattva-mahāsattva Maitreya, “Maitreya, here today, the Bhagavān, gazing at a rice seedling, spoke this aphorism to the bhikṣus: ‘Bhikṣus, [just like this seedling was born from causes and conditions, the twelve nidanas occur in succession to one another. Verily,] whoever sees dependent arising sees the Dharma. Whoever sees the Dharma sees the Buddha.’ [...] Maitreya, what is the meaning of this aphorism spoken by the Sugata?

1) What is dependent arising? 2) What is the Dharma? 3) What is the Buddha? 4) How does one see the Dharma by seeing dependent arising? 5) How does one see the Buddha by seeing the Dharma?”

The bodhisattva-mahāsattva Maitreya then replied to the venerable Śāradvatīputra, “Venerable Śāriputra, you want to know what dependent arising is in the statement made by the Bhagavān [...]

Well,

1. the phrase dependent arising means that something arises because something else already exists; something is born because something else was already born. [...]
2. what is the Dharma? The Dharma is the eightfold path of the noble ones [...] This eightfold path of the noble ones, combined with the attainment of its results and nirvāṇa, is what the Bhagavān has called the Dharma [...]
3. who is the Bhagavān Buddha, [the Dharma-Born]? A buddha is so-called because of comprehending all dharmas; is endowed with the wisdom eye of the noble ones and the body of Dharma [...]
4. how does one see dependent arising? On this point the Bhagavān said, ‘One who sees dependent arising as constant, without life force, devoid of life force, true, unmistaken, unborn, not arisen, uncreated, uncompounded, unobstructed, imperceptible, tranquil, fearless, incontrovertible, inexhaustible, and by nature never stilled, [...] clearly understands the Dharma of the nobles ones, and
5. by thus acquiring such right knowledge, sees the Buddha -- the body of unsurpassable Dharma.’

[...]

[...] there are four links that serve as the cause for assembling this twelvefold dependent arising. What four links? Namely, 1) ignorance, 2) craving, 3) karma, and 4) consciousness.

1. Here, what is ignorance? That which perceives the six elements [earth, water, fire, wind, space, and consciousness] as a unit, a lump, permanent, constant, eternal, pleasurable, a self, a being, a life force, a creature, a soul, a man, an individual, a human, a person, me, and mine, along with the many other such variations of misapprehension, is called ignorance. [...]
2. The presence of such ignorance brings desire, aversion, and delusion toward objects. [...] three types of [karmic] tendencies accumulate: those that lead to meritorious states, those that lead to unmeritorious states, and those that lead to neutral states.
3. Karma [resulting from karmic tendencies] and afflictions [i.e. ignorance, craving, and pursuit of objects] cause the seed of consciousness to grow [...] [Consciousness dwells in the impressions produced by karma which are then deposited in the consciousness as representation of objects]
4. That which distinguishes between individual objects is consciousness. [...] When the seed of consciousness grows, planted in the field of karma, moistened by the water of craving, and strewn with the manure of ignorance, the sprout of name and form manifests.

[...] there is nobody at all who transmigrates from here after death and is born elsewhere, and yet, because there is no deficiency of requisite causes and conditions, the result of karma nonetheless manifests [...] although things are devoid of owner, devoid of ownership, ungraspable, space-like, and their nature is the mark of illusion, because there is no deficiency of requisite causes and conditions, the seed of consciousness born of karma and afflictions will nonetheless produce the sprout of name and form [...]

[...] “Thus, this twelvefold dependent arising — which comes from several different causes and from several different conditions, is neither permanent nor impermanent, is neither compounded nor uncompounded, is not without any cause or condition, is not an experiencer, and is not something exhaustible, something destructible, or something that ceases — has proceeded from time immemorial, without interruption, rolling along like a flowing stream.

[...]

Venerable Śāriputra, whoever sees with perfect wisdom this dependent arising, perfectly taught by the Bhagavān, as it actually is — as always and forever without life force, devoid of life force, true, unmistaken, unborn, not arisen, uncreated, uncompounded, unobstructed, imperceptible, tranquil, fearless, incontrovertible, inexhaustible, and by nature never stilled — whoever fully and truly sees it as unreal, vain, hollow, unsubstantial, as a sickness, a boil, a thorn, as miserable, impermanent, painful, empty, and no-self, [thereby restricting the power of ignorance-produced karmic tendencies] -- such a person does not reflect on the past thinking, ‘Did I exist in the past, or not? What was I in the past? How was I in the past?’ Nor does such a person reflect on the future thinking, ‘Will I exist in the future, or not? What will I be in the future? How will I be in the future?’ Nor does such a person reflect on the present thinking, ‘What is this? How is this? Being what, what will we become? Where does this being come from? Where will it go when transmigrating from here at death?’
Whichever dogmas mendicants-and-brahmins hold throughout the world, whether they involve belief in a self, belief in a being, belief in a life force, belief in a person, or belief in rites and rituals -- such dogmas, prone to agitation and dullness, are all abandoned at that time. Fully understood as false, these dogmas are severed at the root and wither like the head of a palm tree, never to arise or cease in the future.

[...]

The meaning of this, as I understand it: just as someone looking at a moist seed in the ground sees the potential sprout - same way someone looking at the seeds of ignorant consciousness in the ground of karma sees the inevitable arising of individual experience, and someone who understands this dependent origination of individual experience - necessarily understands ignorance, craving, and origination of suffering. Since s/he understands how it originates -- s/he understands how it can stop. S/he understands the ground, the goal and the path. This understanding is called "seeing the Dharma".

Seeing the Dharma, there is no more ignorance, no craving or aversion, no attachment, no selfish goal-making, no I-projecting, no conflict between "is" and "should", no suffering, no birth and no death. Whatever remains is suchness.

Seeing the Dharma is seeing Buddha, because Buddha is born from the seeds of Dharma and Dharma is spread by Buddha, just like with rice plant and rice.