AMV is a term that's been around for a LONG time, and used by the people who make such things.
MY problem with the trope is it's fan-myopic approach to discussing the subject matter: It seems to have a heavy emphasis on Disney animals, when, a search for AMV reveals that the subject matter is anime-based. In fact, AMV seems to stand for ANIME music Video, not "Animated" (the contention being that the music is set to Japanese cartoons). As i search for "AMV" anywhere, the results are overwhelmingly anime in nature. I can't even find ANY results that match what this page seems to be talking about. I search for "AMV" on youtube and the results are mostly Bleach, Haruhi Suzimaya, Final Fantasy 7, Naruto... not a single "101 dalmations" or anything of the sort. Perhaps all that stuff needs its own page: Animash"
I would vote for "Fan Vid" to be turned INTO "AMV", because "AMV" is the colloquial term used for the media.
It may not want to be what this site wants, but that would be like refusing to call Star Trek "Star Trek" because we don't like the use of the word "Trek" (for whatever reason, just making up a possibly strawman example)