The “hypocrisy” makes perfect sense if you read the DMCA safe harbor provisions—YouTube gets a free ride because of the terms of the DMCA, which says that if the online provider doesn’t know about the copyright infringement, then they basically are safe from being sued as long as they take it down when requested to by the copyright hoder.
Is it hypocrisy? How so? They put up the requisite “we don’t condone copyright infringement” messages, but everyone knows that’s a nod towards the courts. You might as well criticize the company for making q-tips as hypocritical because they say not to use them to clean your ears (and give dozens of examples of other potential uses people might have for them, when of course everyone uses them to clean their ears).
They don’t get any more or less of a free ride than anyone else. It has to do with them being a big system that hosts user content. If you set up something similar you’d be covered by the same laws.
(As for fair use, it doesn’t really matter here. It’s a defensive activity; YouTube would never want to rely on it because it would mean they’d have to be in front of a judge to defend it. Why would they allow themselves to get into such a position over a Muppets clip? They’d rather just take it down.)