Yeah, but that takes the punch out of the theorem. It's saying, "hey, sometimes you have really screwy preferences, too bad."
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?
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".
That is all the punch he theorem has. Arrows theorem shows that aggregate preferences have ties even when individuals don't, and strategic voting can tip the results in those cases.
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?