I wouldn't be surprising at all if some doctors in ancient China got executed for reasons like that.

But it's essentially the same as in Western medieval ages. There were certain things doctor's knew how to do, and they actually managed to help - those are the things that got developed further into modern medicine. And then there was a bunch of stuff that people just made up due to lack of scientific standards. But nobody knew better, so they still did it, especially to noble families (as they could afford doctors). Think about blood-letting or cupping therapy.