The writer of this article had the definition right early on. The term "anime" refers only to animation created by a Japanese animation team, produced in Japan, and developed for a Japanese audience. It describes the work's geographic origin. You shouldn't be classifying Korra as part of the anime genre because "anime" itself isn't a genre.
Korra and Avatar aren't anime, because they weren't made by and for Japan. That does not make them bad shows and it doesn't lessen their legitimacy as great works of fiction. The shows certainly take a lot of inspiration from Japanese shows, in particular the Shonen genre in anime. Anime itself is not a genre, so even calling something a "western anime" or an "American anime" doesn't really work. Japanese animation has a wide variety of genres. You have westerns, sci-fi, horror, mystery, action, and even sports. "Anime" is simply a term to use to identify it's country of origin.
The way I see it, a good show or movie is a good show or movie. It doesn't matter what country it came from or what art style it uses. I enjoy shows like Avatar and Korra just as much as I enjoy Full Metal Alchemist, Cowboy Bebop, and FLCL. We don't need to validate shows by saying that they are "Western-anime", and therefore somehow better than other western animation. The shows should be judged by their own merits or lack there of. At least that's my opinion.