Regardless, within the set of all animation -- we have a clear view on what is definitely "anime". Never in a million years would I question something like Haruhi, Clannad, and even Akagi as not being "anime". For all intents and purposes, series like those are unquestionably "anime". If someone were to come out and say that any of them were "Made in China", that viewpoint will not change.
In contrast, I had long viewed Avatar as an anime, despite not watching it. However, after I watched it fully, the story line had a feeling of anime; but the series falls short visually -- even though it tried. Of course, I was disappointed. The only bright side aims as Avatar being the closest any American studio has come to making anime.
For a long time, I have been going on about the categorization on a visual basis. Story line arguments on this topic have long been irrelevant, because any written story can be ported (and adapted) into any medium. Thus, story line and plot is moot.
However, I would question Crayon Shin Chan, as a Japanese cartoon. Rather than as an anime, because visually, it is on the same level as Spongebob. Many will retain Shin Chan as anime, based on previous points of "production in Japan" and "made for the Japanese audience". Well, out of all the "anime", Shin Chan is one of the most "cartoony".
And so, given this Venn Diagram:
What goes in that bluish region?
Then there's another factor. You watch something. Does it "feel" like "anime" or not? For Avatar, it did not. For many examples we can name around here, that's an obvious yes. If any non-Japanese studio can produce this same "feel", then they have something going in the "anime" direction. For now, no one other than a Japanese studio can produce this.
I could start pointing at Pixar, but Pixar style-animation is a different set of animation all-together. Part of me is curious as to what would happen if some Japanese studio starts utilizing the 3-D graphics style (CGI) for 100% of an animation project, especially regarding humanoid characters.