That's a good question and my understanding of it is no -- they do not eat meat that is still rare.  There was a bit of an minor diplomatic error over this recently when the head of the country went on a state visit to a Western country that I won't name and unwitting head of this Western government served the entire Chinese delegation very pricey aged steak (again, the Chinese will not eat old meat -- there is the first meat) cooked so that it was extremely rare.  Didn't exactly win any friends, to tell the truth. (and the rest of the dinner was a "real down home" kind of dinner most of which the Chinese would find not to their likings).

So yes, it is not your friends -- not at least in my experience.

They don't. I think it's a mix of culture, and the fact that local butchers and supermarkets always break the cold chain, and hyigene isn't exactly great, so the meat better be well-cooked.

At many western type restaurants and steakhouses they ask how you want your steak cooked. They use a scale of 1-10 with 10 being the most cooked.  I find most of my Chinese friends will order between 6-8.     
So there are some people who will eat rarer meat, but nothing bloody.

Most Chinese people I know do not like rare meat.  For pork and chicken, of course I can understand this, but lamb and beef....

Mr Spoon is correct though.  I think it has to do with the sometimes less than sanitary conditions, the lack of a cold chain, and cultural preference.

Beef here isn't really that good anyway.  I usually get some nice aged beef from Australia.

I guess eating it rare never crosses their mind as they chop it up in such tiny pieces that it cooks in a matter of seconds anyways.