i would not go to a Chinese hospital for just a check up. If I get sick use the insurance other wise either pay for it or go home, since its not an emergency it can wait. If you have a serious problem normal health insurance wont fly you home.
Also the costs in hospitals for normal stuff are cheap I broke some ribs doctor visit , xrays etc was only a couple of hundred rmb , same with a full on flu antibiotic drip etc
not worth the paper work to claim. so really health insurance is only good for real emergencies that might be expensive. but that is what the travel insurance covers .
I guess there are points either way just seems the best for me. But I am not tied to a 9 to 5 job I can come and go as I please.