I'm going to have to say, being Asian American and seeing a lot of films, a lot of movies are better off not hiring Asian American actors. I'm going to use the movie War (Jet Li, Jason Statham) for an example. In short, the movie was centered around the "Yakuza", and to make it authentic, they hired pretty much any and every Asian American actor they could to play these supposedly "Japanese" roles. Their performance was beyond horrible.
The thing about Asian American actors is that they typically get spotlighted in films because they are Asian. For instance, in War, I was like "That's the villain from Rush Hour!". Hollywood does not treat its Asian American actors as just actors. It isn't their acting that gets them the job, but their looks. You tell me how many times Devon Aoki got a role in a movie, but she looks horrible, and she sure as hell can't act. In Japan, everyone is pretty much Asian, so all of the actors are pressured to live up to a certain standard.
The same could be said about Japanese anime. An anime's story might have events that take place in America or something, yet, they have a Japanese person playing the role. You'd probably expect the Japanese to go ape crazy over the fact that it's an Asian guy playing an American's role.
Personally, I think if the actors in the Avatar movie are good actors, then let them be. If you're going to push it, you'll probably get Jet Li and Devon Aoki (and maybe Jackie Chan) playing the lead roles of the film. Hollywood doesn't have a good roster to choose from when it comes to Asian Americans. America also isn't doing a good job at forging new Asian American actors. You could ship Asians overseas and have them film a movie, but their English skills might be terrible, and no one will watch the movie because they don't know who is in it. If it is of so much concern, you might as well have the studio sell its rights to another studio in Hong Kong, and have them film it.