YouTube does have a process to appeal complaints, though I've never had any success with getting them to restore a video.
I created a 'Downfall' parody video two years ago that was yanked by order of Constantin Films the day after I posted it. The notification from YouTube contained a link to dispute the DMCA notice, which I did, claiming fair use. YouTube restored the video almost immediately.
I would have been pretty pissed if I'd received this notice with no way to appeal the takedown.
Google, are you not even going through the motions of "don't be evil" anymore?
A popular youtuber (2,314,015 subs) recently got hit by one of those for his Gangnam style parody.
http://www.youtube.com/watch?v=n6U_dVGRFZQ&list=UUHiJwRo...
He explains the process pretty well.