Well of course. Why wouldn't they? Money and friends aside, they have to do it for people who wield power like China's upper echelon or the NSA. If they say no, they will be shut down in those markets.
Then to put it more simply, large companies must tow to influential requests because that influence determines the flow of money. Govt, private, or individual -- doesn't matter.
And Facebook is not actually shut down in China. It's partially blocked and working on a censorship project to reinstate itself there.