Can a Buddhist truthfully say, "You insulted / offended / angered / hurt me?"

"What is the contemplative's doctrine? What does he proclaim?"

"The sort of doctrine, friend, where one does not keep quarreling with anyone in the cosmos with its devas, Maras, & Brahmas, with its contemplatives & brahmans, its royalty & commonfolk; the sort [of doctrine] where perceptions no longer obsess the brahman who remains dissociated from sensuality, free from perplexity, his uncertainty cut away, devoid of craving for becoming & non-. Such is my doctrine, such is what I proclaim."

When this was said, Dandapani the Sakyan — shaking his head, wagging his tongue, raising his eyebrows so that his forehead was wrinkled in three furrows — left, leaning on his stick.

Madupindika sutta

For most Buddhists, in sphere of their ideas: no (but whether they would say that in practice is another topic).

In regard of the teaching of the Buddha, phenomena have causes: see this answer about the cause of pleasure and pain here.

To illustrate that with a nice story:

Su Dongpo Story

Su Dongpo was an avid student of Buddhist teachings. He was quick-witted and humorous; as a Zen Buddhism follower he was very serious and self-disciplined. He often discussed buddhism with his good friend, Zen Master Foyin. The two lived across the river from one another.

Following is an interesting and famous story about him and Zen Master Foyin.

One day, Su Dongpo felt inspired and wrote the following poem:

稽首天中天， 毫光照大千； 八风吹不动， 端坐紫金莲。

I bow my head to the heaven within heaven, Hairline rays illuminating the universe, The eight winds cannot move me, Sitting still upon the purple golden lotus.

The “eight winds (八风)” in the poem referred to praise (称), ridicule (讥), honor (誉), disgrace (毁), gain (得), loss (失), pleasure (乐) and misery (苦) – interpersonal forces of the material world that drive and influence the hearts of men. Su Dongpo was saying that he has attained a higher level of spirituality, where these forces no longer affect him.

Impressed by himself, Su Dongpo sent a servant to hand-carry this poem to Fo Yin. He was sure that his friend would be equally impressed. When Fo Yin read the poem, he immediately saw that it was both a tribute to the Buddha and a declaration of spiritual refinement. Smiling, the Zen Master wrote “fart” on the manuscript and had it returned to Su Dongpo.

Su Dongpo was expecting compliments and a seal of approval. When he saw “fart” written on the manuscript, he was shocked . He burst into anger: “How dare he insult me like this? Why that lousy old monk! He’s got a lot of explaining to do!”

Full of indignation, he rushed out of his house and ordered a boat to ferry him to the other shore as quickly as possible. He wanted to find Fo Yin and demand an apology. However, Fo Yin’s door closed. On the door was a piece of paper, for Su Dongpo. The paper had following two lines:

八风吹不动， 一屁弹过江。

The eight winds cannot move me, One fart blows me across the river.

This stopped Su Dongpo cold. Fo Yin had anticipated this hot-headed visit. Su Dongpo’s anger suddenly drained away as he understood his friend’s meaning. If he really was a man of spiritual refinement, completely unaffected by the eight winds, then how could he be so easily provoked?

With a few strokes of the pen and minimal effort, Fo Yin showed that Su Dongpo was in fact not as spiritually advanced as he claimed to be. Ashamed but wiser, Su Dongpo departed quietly.

This event proved to be a turning point in Su Dongpo’s spiritual development. From that point on, he became a man of humility, and not merely someone who boasted of possessing the virtue.

The Lord Buddha said those who accuse another falsely with slanderous speech go to hell. Keeping this in mind, a Buddhist should not be offended.

He goes to hell, the one who asserts what didn't take place, as does the one who, having done, says, 'I didn't.'

They stab with their words — people unrestrained — as they do, with arrows, a tusker gone into battle. Hearing abusive words spoken, one should endure them: a monk with unbothered mind.

Sundarī Sutta

I think it is your responsibility to stay calm. But first listen carefully, because maybe the person is telling you the truth in an aggressive way. So if he/she is telling the truth, accept it. If not, ignore and stay calm. There is no reason to feel angry.

Can a Buddhist truthfully say, “You insulted / offended / angered / hurt me?”

A person can say that.

The Dhammapada warns, however, that saying such a thing is not a cure for anger and aversion:

3. "He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.

4. "He abused me, he struck me, he overpowered me, he robbed me." Those who do not harbor such thoughts still their hatred.

On the other hand that doesn't mean that people want to listen to "wrong speech".

I guess a reason why some people ordain (or seek the company of other Buddhists) might be to enjoy the company of a like-minded community. The same Dhammapada (e.g. chapter 23 and chapter 5) says that it's good to have wise friends, but also that "there is no fellowship with the fool".

In any dialog you play two roles: the one who speaks and the one who listens. Buddha gave one common advice that applies to both roles, and two specific ones that apply for each of the two roles.

The common advice (to listeners and to speakers) is:

One does not keep quarreling with anyone in the cosmos with its devas, Maras, & Brahmas, with its contemplatives & brahmans, its royalty & commonfolk;

When you are in the listener's position, the advice is:

If ... there is nothing there to relish, welcome, or remain fastened to, then that is the end of the obsessions of passion, the obsessions of resistance, the obsessions of views, the obsessions of uncertainty, the obsessions of conceit, the obsessions of passion for becoming, & the obsessions of ignorance. That is the end of taking up rods & bladed weapons, of arguments, quarrels, disputes, accusations, divisive tale-bearing, & false speech. That is where these evil, unskillful things cease without remainder.

When you are in the speaker's position, the advice is:

Abandoning divisive speech he abstains from divisive speech. What he has heard here he does not tell there to break those people apart from these people here. What he has heard there he does not tell here to break these people apart from those people there. Thus reconciling those who have broken apart or cementing those who are united, he loves concord, delights in concord, enjoys concord, speaks things that create concord.

Abandoning abusive speech, he abstains from abusive speech. He speaks words that are soothing to the ear, that are affectionate, that go to the heart, that are polite, appealing & pleasing to people at large.

So as they say in Communication Skills 101 courses, you are always responsible for your side.