I see your point and if you go on YouTube you will find hundreds or thousands of copyright infringing material, especially sports highlights. From what I understand Google has a sort of "crawling" system that looks for keywords in the services and flags content that could possibly be violating copyright laws, its then reviewed and taken down. They also rely on users to flag content as well (often these concerned users are people hired by law firms specifically to scour the web for copyright infringement)
These days sporting associations even have P2P live streams to try to control. Justin.tv for example now shuts down any live matches it catches being shared through their service.
I think this could be an interesting opportunity for Google through YouTube to ramp up to TV subscription services. I know that if I were to live in the US I would get rid of cable or sat tv if I could just use Hulu and had a competitive sports offering online!