This is a question of linguistic or encyclopedic meaning/knowledge.
I think that "Everyone kills someone" actually is still ambiguous, linguistically. Imagine a crazy world in which you could kill people multiple times-- or even a not to strange video game. "On level one, everyone [each player] kills someone [the bad guy named 'John']."
This does get into issues of coercion (does the sentence/context force the words to change meaning?) and normal usage. It's very similar to a sentence like "I drank the potato." It's not necessarily incoherent in some ways, but as a whole idea it's wrong. It's unclear whether we want to call that a syntactic or semantic or pragmatic effect! The thing is... in a weird cartoon you could imagine Mickey Mouse drinking a potato, with the right kind of animation. So... what is it? Grammatical?
This is, of course, what Chomsky discussed with "Colorless green ideas sleep furiously."
Personally, I disagree with him. I think that's a perfectly fine (but effectively useless) English sentence; I even think the meaning is coherent, though we as speakers in the real world may not be able to fully comprehend/contextualize it. But, again, think of a cartoon. I could try to draw that!
As for a more specific point about the verb "kill" versus "love", there's an issue of Aktionsart (or Lexical Aspect) including telicity and so forth. In that case, it also just happens that "kill" is a unique event. Technically another verb like "hit" is also similar for Aktionsart and would be unique in each instance, but then there could be unrelated instances. It's sort of a sloppy reading to have "Everyone hit someone" for one person, because that would be multiple hittings. Actually I suppose not-- you could have everyone punch you in the face at the same moment... is that just one hitting? Ha. But then in that case, as PhantomSoul hinted at, you can get that reading fairly easily I think-- "Everyone killed someone by pushing him off of the cliff together". Only the separate events reading is unavailable, actually.