Add my vote to foregoing insurance. The OP is going to be, for the most part, in well-developed cities in China that compare to any major city in the west. Chinese health care is paid for out-of-pocket (the Chinese don't have health insurance), but costs when measured against the American dollar are quite low and affordable.
I also agree that the State Department webpage tends towards hysteria. I've been going to China once or twice a year for more than 12 years (my wife is Chinese and we visit friends and family there). I would not be worried, in the least, about seeking medical care there if I needed it. The doctors speak "medical English," (I know this because my father-in-law is a retired surgeon) and, I suspect, the OP's tour company can provide someone to assist with basic translation needs in the event of an emergency.
Go enjoy China and don't worry -- it's a wonderful country with wonderful people and a truly amazing place for Americans to visit.