Youtube have deals with many major content groups which gives the groups access to disable a video without any verification process. It's entirely plausible that some intern at UMG is going through big lists of songs, searching for their existence and accidentally flagging ones that aren't actually property of UMG, or maybe they're abusing the power that they have to remove stuff they just don't think should be there (but has a legal right to be).
Nope, I asked my friend who worked at Youtube about this. He told me that they have to remove every video the label asks to have removed. Seems like a fantastic system. Surprisingly another American legal convention that favors a monsterously large corporation and shits on the individual citizen.
I believe they have the ability to remove any video yes, but I assume there are agreements; after all Youtube are not required to provide this, if they were to abuse it beyond what can be explained away with "dumb intern" or "oops wrong video" Youtube may decide to cut it off, but obviously Youtube get lots out of such a deal -- like Vevo, so who knows!