Whether it is defined as an anime or not is completely, utterly arbitrary.
In fact, there is no firm definition of what "anime" is, it is more of a slang, and could either refer to:
1) Cartoons made in Japan
2) Cartoons made with typical Japanese cartoon style
In this sense, if a Japanese animation team decides to do something very non-anime-like, it could still fall into the first definition but not in the second. On the other hand, if somebody outside Japan would decide to create an animation that mimics the typical Japanese style, it falls under definition number 2.
And that is it. It is incredible how people find the time and energy to discuss something as arbitrary as this, and more so without any sort of real argumentation. It only comes down to language and what words mean at some point in time, it is not an exact science where you invest a lot of energy to defend a proper scientific proposition that's as true as ever, language is ever changing.
All this being said, Myazaki's films are at some points BARELY anime by the 2nd definition, but definitely so by the 1st definition.
Avatar is ABSOLUTELY NOT anime by 1st definition, but is VERY MUCH SO according to the second definition.
Country of origin is an extremely arbitrary thing if it does not necessarily dictate the shape or form of content of some media. In said edge cases, that's shown to pretty much be the case upon any closer style inspection.
Therefore, is Avatar an anime? It shares many technical similarities with typical Japanese animation therefore, let's say it is. Is every single cartoon in Japan an anime, DESPITE maybe not having any typical technical attributes that Japanese animation has? No. And this is all to separate things into categories by similarity of form, rather than country of origin.
After all, "anime" is more so a slang word, an abbreviation of Japanese pronunciation of "animation", and in Japan it refers to all animation, not just what is considered to be "anime" in the western world. This goes to further challenge the idea that language is something stiff and that those definitions are of particular importance. After all, we all use language just for convenience and ease of communication, therefore, again, it is more meaningful and purposeful to separate things by form, rather than simply country of origin.
Here is My Anime List's search result for "Legend of Korra"
http://myanimelist.net/search/all?q=Legend of Kora
It is not anime.
MyAnimeList, although a very useful site, is not the absolute authority on defining English (or any) language.
From this post onwards, all posts regarding what anime is or is not will be 'moder8ed' out of the thread since apparently Squiggy is watching over this thread. I am only writing and putting this out there to make sure that people understand what the thread refers to.