If we remove the adjectives formed from proper nouns, turn the nouns into "people", turn the verbs into "bully", and add a pronoun and an adjective, we get

    people whom other people bully bully people.

This makes sense.

But when we remove the pronoun and adjective and we get

    people people bully bully people

which is as far I can tell gibberish (without changing meanings such that they don't correspond with the original sentence). It can't have anything to do with many people persons, because in the original there's an adjective there.

If we assume that, just as there are social adept people, whom we call "people people", there are also socially adept buffalo called "buffalo buffalo", we can get "Buffalo buffalo buffalo buffalo buffalo". But to go beyond that is to claim an incoherent sentence missing many words is coherent and grammatical.