I was with Ibn 'Abbas, and Ibn 'Abbas saw the Messenger of Allah (ﷺ) doing like this, and it is also said that the words are: He (the Holy Prophet) offered prayer; and the word" people" is not mentioned.
Sahih Muslim Book 3, Hadith 122
← Previous Hadith The Messenger of Allah (ﷺ) dressed himself, and then went out for prayer, when he was presented with bread and meat. He took three morsels out of that, and then offered prayer along with other people and did not touch water.

Sahih Muslim Book 3, Hadith 121 Next Hadith → A man asked the Messenger of Allah (may peace he upon him) whether he should perform ablution after (eating) mutton. He (the Messenger of Allah) said: Perform ablution it you so desire, and if you do not wish, do not perform it. He (again) asked: Should I perform ablution (after eating) camel's flesh? He said: Yes, perform ablution (after eating) camel's flesh. He (again) said: May I say prayer in the sheepfolds? He (the Messenger of Allah) said: Yes. He (the narrator) again said: May I say prayer where camels lie down? He (the Holy Prophet) said: No.

Sahih Muslim Book 3, Hadith 123