Update: Received a response from a YouTube spokesperson which makes this a little more interesting.

Our partners do not have broad take-down rights to remove anything they don't like from our service. In limited cases, if they so choose, and based on exclusive agreements with their artists, partners can take down live performances.

That confirms some of what I thought: that UMG does not have the right to take down any videos (as people keep implying), but that it may be able to take down some videos. The new bit of info is that it's just live performances. So, that would suggest UMG is even slimier. They tried to claim that those video clips of artists in the Megaupload song were "live performances." That's clearly bogus.