Just to add my two cents in here, we had to make this choice as well on Tom's a while back. Nearly every site with any forum community in it has to make this choice, and ultimately makes the choice to disallow YouTube ripping stuff. It's kinda a no-brainer. Firstly, it's technically iffy legal territory, and that's generally bad news. Secondly, it's Google asking. They aren't demanding, like the guys with the DMCA requests that hammer a forum, but rather just politely asking. And they make it pretty clear. They aren't even saying they'll punish you or send you a demand about it. They just say they won't be partners with you. It's certainly the nicest request I've ever gotten from a company about content objected to on a forum. Thirdly, it is Google. Google can hurt you permanently in the land of the intarwebs. Being able to post a link to something you can get literally anywhere else (including, note, GOOGLE search), is a microscopic concession (if even that) and one gladly made by anyone confronted with the choice who has the well-being and survival of their community in mind.
Now, if it was something like a thread critical of Google's methodologies, or their corporate practices, or even the Google doodle of the day, and they asked for a takedown, I'm sure the response would be to politely disincline to acquiesce across the board.