They are protected under the safe harbor porvision of the DMCA which basically says that if someone says "That's my stuff, take it down" they have to take it do

They are protected under the safe harbor porvision of the DMCA which basically says that if someone says "That's my stuff, take it down" they have to take it down. However if no one complains, YouTube can argue that millions of videos are added everyday, they can't possibly screen them against every piece of copyrighted music/film ever made.