‘Creep’ by Radiohead is a great song. Eliza Lumley does a good cover. I imagine Prince would too. He performed the song at a concert, someone videotaped his performance, and then posted it on YouTube. Prince sent a DMCA letter and got the video taken down. Thom Yorke of Radiohead found out and allegedly asked Prince to restore the video, indicating that Radiohead was the copyright owner and he had wanted to see Prince’s version.
The video could, in theory, infringe various rights. It could have been a breach of contract if the venue prohibited filming; it might violate Prince’s right of publicity or trademark. Prince didn’t own the copyright in the composition so that’s out. If Prince had recorded the performance, the video wouldn’t be a copy of that recording. As this EFF post points out, the video may violated the anti-bootlegging statute; however it’s my understanding that that is not a copyright right under DMCA. If Prince had recorded his performance that would have ‘fixed’ his choreography. Maybe his set is copyrighted (his guitar is a registered copyright (and trademark)). So it seems that Prince may very well have a good faith belief that he owned a copyright that was infringed by the video.