That’s how language works, yes. Otherwise, every sentence with the word “everybody” in it would be false.
eve·ry | ˈev(ə)rē | determiner (preceding a singular noun) used to refer to all the individual members of a set without exception: the hotel assures every guest of personal attention | [with possessive determiner] : the children hung on his every word.
>Otherwise, every sentence with the word “everybody” in it would be false.
No. "Everybody over there" is not false if it refers to everybody over there for example. If you use everybody to refer to some people, then that is your poor word choice.