Anime is a style. I've never, ever heard that it has to be produced in Japan. Avatar so closely follows the style that in my mind, it falls under that category.

Also. Anime originated from American works. The big eyes came from Bambi and Mickey Mouse, and the unrealistic head set on a realistic body came from Betty Boop. So it isn't some ancient, sacred art style that only the Japanese are savvy to. America had a huge influence over it. Yes. We sloppy, inferior, useless, overweight, greedy Americans blew our load into the oh-so-superior Japanese creative fuck-caverns.