In a nutshell, yes, Neo's example of Jesus punching someone is a good example, unless you're referring to the Jesus as a recurring character in Family Guy, in which case I'd call it a moo point.
Anyway, the Avatar is essentially the Jesus of the Avatar world, and because the Avatar is supposed to follow the Jedi way of love and peace and harmony, him beating the living shit out of someone, no matter how evil, is going to put a bad tomato on his name.
Though you could argue that history is written by the victors, as it almost always is; a revolutionary war is only called a revolutionary war if said revolution is successful; otherwise it would be called a "revolt" or an "uprising" or something like that that would probably give anyone the impression of it having been unsuccessful. In which case the Avatar could say that "senseless violence" would have been the only way (which any person with any sort of common sense would call as flying bison dung, or whatever their term for "bantha fodder" is).
My point is, the Avatar would never resort to senseless violence, as that is not what the Avatar stands for and holds the spirit of; remember, Raava is the Avatar spirit, and she could (theoretically) leave her human host at anytime if she deems her host to be unfitting of being the Avatar.
When I said "in a nutshell" I might have meant the shell of a walnut with nut cancer, because look at the size of this post.