Good question. It was your sick scenario, I await your answer...
All right, since you have deferred to me to answer my own question, I will....
Because the desired goal is worth it, and because we have at our disposal diplomatic bargaining chips that could be offered up in exchange for what we desire. A deal that the Chinese could promote as being a tradeoff for their capitulation that results in being beneficial to them could very realistically be worked out. As long as the taint of perceived caving to protests on the Chinese government's part isn't a factor, that is.
LOL! You set the whole straw-man up, why shouldn't you answer to it?
Because the desired goal is worth it, ...
Why is it "worth it"?
Because if we don't appear to sufficiently apologize and throw a little woman with nothing more than a banner and some words in jail because you felt, ahem, "threatened" you're going to send a present of human livers and attempt to place the blame for that package on us?
Why should we kowtow to your blackmail?