I'm sorry, but everyone who creates art, automatically has rights to it. You may not have rights to the anime or the song, but you've created something with them, thus giving you the rights to your AMV. Agree with it or not, it's objectively true.
Not to copyright lawyers. What they see is copyright infringment and not art.
To put it simply, we don't have any kind of rights to our amv's. All we have is respect for fellow creators and give credit where it is due.
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The Thrill of The Kill Is Alive and Well!