As far as most anyone is concerned, monitoring YouTube for user-initiated copyright violations to send takedown notices is precisely what the DMCA was intended to be used for.
Agreed. My then-3 year old daughter danced to the tune of Da Funk and I uploaded it. The sound was removed, even though it was in the background. It was Fair Use for sure.
Shame on YouTube, quite seriously - I didn't cost Daft Punk anything!