Why is 'attention' ('manasikara') included within 'nama-rupa'?

Is it true?

The uninformed run-a-mill-person, touched by form (sound, smell, tast, bodily sensation, idea - here of seeing a fault) on the eye (ear, nose, tongue, body, intelect), pays it wrong attention. Having payed wrong attantion, not having considered it wisely, taking attention as real, lasting, statisfaction, it as "mine", grasps after it, take hold on it, and make it to a matter. So after becoming, mind and matter come to birth.

If a little wisely, one would see, what ever comes to birth, what ever one takes on attention in the mind-matter sphere, all this is subject to decay.

But the uninformed run-a-mill-person, caught in pride and conceit, is incapable for proper attention, incapable to understand mind eg. feeling, perception, intention, contact & attention.

My person tells you, it would be better if he would take form as lasting, satisfacting, for his own, self. Why? Because he could see it's decay.

And how does a disciple of the Noble One considers, acts and pay attention?

Touched by form... touched by attention on the intellect, he gives not unwise ("selfinvolved") attention, considering "this is suffering, this is the cause the origin of suffering, this is the cessation suffering, this is the way leading to the cessation of suffering", giving proper attention in "this has come into being", gives proper attention, does not take grasphold of it. Not taking on it, it does not become matter for mind, nama-rupa does not come into be and stress and suffering is end, released.

Very good & helpful answers, including @Saptha Visuddhi's reference to ayonisomanasikāra:

They are all activity of nāma-rūpa happening only in the present. From this ‘sampassa’ (san+passa) comes Ayonisomanasikāra.

I was giving attention to this in meditation this morning and I decided upon this similar answer:

Dependent origination arises from ignorance &, of particularly relevance is, the absence of mindfulness & wisdom at sense contact. About this, MN 38 states:

On seeing a form with the eye, he lusts after it if it is pleasing; he dislikes it if it is unpleasing. He abides with mindfulness of the body unestablished, with a limited mind and he does not understand as it actually is the deliverance of mind and deliverance by wisdom wherein those evil unwholesome states cease without remainder.

In respect to this lack of mindfulness & wisdom, AN 10.61 states:

Lack of mindfulness and clear comprehension, too, has its nutriment; it is not without a nutriment. And what is the nutriment of the lack of mindfulness and clear comprehension? 'Unwise attention,' should be the answer.

When unwise attention (ayoni­so­ma­nasikāro) prevails, it will make prevail lack of mindfulness and clear comprehension.

AN 10.61

In summary, I think attention is included within nama-rupa because ignorance conditions/prepares nama-rupa for unwise/ignorant attention, which in turn will make sense contact unwise/ignorant.

Why do we think 'attention' ('manasikara') is included within 'nama-rupa'?

Attention is a mental factor (cetasika) that arises based on several other factors, one of those being intention (cetana). It performs one of several cognitive functions that allows for consciousness of an object to arise. This can be experienced through the practice of insight meditation. As this is purely a mental function it is included in Nama-rupa, i.e. the Nama-aspect.

In walking meditation the meditator can experience the four great elements as actual processes (ultimate realities), e.g. the feeling of lightness that occurs in the lifting-phase of the foot. That right there is the experience of the fire element. The awareness of that feeling of lightness belongs to Nama and that feeling can only be experienced if attention is present and performing its mental function. Again, we see why attention can be included in the Nama-aspect.

So to answer the question: Attention is a mental factor. Mental factors belong to Mentality. Mentality is the Nama-aspect of Nama-rupa.

Citta and cetasica can not work their job without attention.

You can not know/memorize/feel anything, if you don't have attention on it. No one memorize stuff, that they never mind.

Full translation is:

Vedanā, saññā, cetanā, phasso, manasikāro — these (example of 53 lokiya-nāma) are called (53) nāma.

The 4 mahābhūtā rupū and (24) rūpā, that depend on mahābhūtā rupū, — these are called (28) rūpa.

These both, nāmā and rūpā, are called nāmarūpa.

Source:

Vedanā, saññā, cetanā, phasso, manasikāro - idaṃ vuccatāvuso nāmaṃ. Cattāri ca mahābhūtāni catunnañca mahābhūtānaṃ upādāya rūpaṃ. Idaṃ vuccatāvuso rūpaṃ. Iti idañca nāmaṃ idañca rūpaṃ - idaṃ vuccatāvuso nāmarūpaṃ.

So, nothing to doubt. Pali is clear.