YouTube doesn’t really have legal troubles. This article explains how part of the DMCA actually makes YouTube’s way of doing things explicitly legal. That is, the runners of a service aren’t liable for hosting infringing content as long as they a) don’t know about it and b) remove it promptly when they are notified. YouTube seems to be pretty responsive when copyright holders complain (sadly, they took down a bunch of Daily Show and Colbert Report clips) so they — and Google — should be alright.