The claim is, of course, bogus. Wilkinson doesn't have rights over anything in the video: he didn't film it, and the song belongs to EMI. It's likely that he just wanted to stem the tide of this embarrassing video, and knew that he could do so in a few steps with YouTube's takedown tool. Whether or not he believes he does have some copyright stake here is unclear, but hopefully he knows better than to pursue things further, because he could end up facing liability for copyfraud. Unfortunately, this is how notice-and-takedown systems work: free speech can be easily censored, at least temporarily, by anyone for any reason.

Copyright does not exist to save people from embarrassment, nor does it even apply in this case—but in the ownership culture of intellectual property, the average person seems to think they have some innate right to control every use of their image or even any reference to their existence. It's not like this will make a difference anyway: plenty of people have surely made copies of the video by now, and it'll be back soon enough (possibly with autotune, or synced to My Little Ponies clips). Sorry Robert Wilkinson: there's no escape from reality.

"It seems like a mistake has been made."