Copyright owners already have power under the DMCA laws to ask a website to take down material they own. Youtube even has tools that make it easier for them. They have abused those tools too and taken down videos they don't in any way own.
Recently Megaupload, which is being sued by Universal, had a video they produced with Will.i.am, Puff Daddy and other famous hip-hop artists pulled from Youtube. Universal claimed they owned the copyright but it was all original work produced for Megaupload, Universal had no claim on the song.
Mystery surrounds Universal's takedown of Megaupload YouTube video | InSecurity Complex - CNET News