Prince performs a cover of the Radiohead break-out hit "Creep" at the Coachella Music Festival. Fans post video of the public performance on YouTube. After already receiving thousands of hits, YouTube removes the video at Prince's label's request; however, Radiohead wants YouTube to "unblock" the video. What does YouTube do?
Billboard addressed the issue: Observing first that "the posted videos were shot by fans and, obviously, the song isn't Prince's", Billboard continues, "Whether the same [DMCA notice] could be done for a company not holding a copyright is less clear, but Yorke's argument would seem to bear some credence according to YouTube's policies".
So, notwithstanding your views on the DMCA, who has priority under the notice and take-down scheme -- the owner of copyright in the sound recording (Prince), or the owner of copyright in the underlying composition (Radiohead)?
Because this was a live performance, it is highly unlikely that there was any sort of publisher/performer agreement other than the public performance license (compositions) the venue pays.
Another tangential issue is Prince's right of publicity/privacy. Most performers prohibit video/flash-camera at their concerts, and in fact, Prince prohibited the standard arrangement of allowing photographers to shoot near the stage during the first three songs of his set. Instead, he had a camera crew filming his performance.
But, rights of privacy/publicity are state laws, and though related, do not come under the Copyright Act's umbrella.
[Update: Marty Schwimmer's post on the Trademark blog re: this "law school fact patter"]