The funniest part of this is that, in my experience, Westerners seem to care more about Anime needing to be Japanese in origin than the Japanese do. It's just their catch-all term for animated media, but if folks REALLY wanna split that hair, I could bring "Japanimation" back into the lexicon.

This is just how loan words work. "Anime" in English isn't a Japanese word that means "animation", it's an English word that means "Japanese animation".