No, of course not. It's really easy to come up with a system that always comes up with "good" results if you rule out "screwy" voter preferences, with a sufficiently restrictive value of "screwy".
"Screwy" in this context means the sort of intransitive situations referred to in the parent of my last comment.
Realistically, that kind of situation doesn't break a voting system. We can say "we don't care about that case -- just pick a random winner then", but it's no longer deterministic.
Is there a stronger version of the theorem that says there's no sane procedure even ignoring those cases?