(Not affiliated with either party, but here's my take)
Simple: clear fair use, and responsiveness to takedown requests.
Take NFL games as an example:
At any given time you can probably find a channel showing any NFL game, but you won't be able to find one that lasts the whole broadcast. That means they're pulling copyrighted content in < 3 hours, which is pretty damn good.
Simultaneously, you can find lots of UGC that isn't pirated on justin.tv (i.e., the site exists for more than piracy).