Well, no, that's not true in the least. The Marvel Cinematic Universe, the film continuity that includes The Avengers, has not so far included any heroes who refuse to kill
None of the Avengers in the movie are crime fighters. None of them have actually gone out to catch criminals.
Tony fights for himself, Thor is a warrior, and Cap was a soldier. The Hulk is probably responsible for countless deaths just from smashing buildings, but the writers try never to mention it.
Also Batman can't go around killing people, otherwise the cops will be after him very quickly.