Based on my shallow knowledge, I have never heard such a story even though I am from China. In ancient China, some doctors travel around to cure poor people because they are poor. Once their names being recognized by most people, they may be hired by royal families become royal doctors. There might be some health specialists working for rich families to keep track of their diets and health plans, such as arrange diets and set up excercise routines, pretty much like a personal trainer. In that case a “personal trainer” could be fired any time, but you still have to go to the doctors if you need it.
I have no cite on this, but I have been told that “ancient chinese doctors” were paid once a year by their “patients”. For the fee, the doctor would make sure you remained in good health for the whole year and make visits to your home when you’d get sick. So, if a doctor was successful, he wouldn’t have to make many “housecalls” and then have more time to care for more patients (meaning more pay) whereas a doctor with many sick patients would be very busy and not have time to see many patients. As for the source, I want to say “The turning point” by Fritjof Capra, but I read it years ago so I could be wrong…
I can’t verify whether the statement about Chinese physicians is true or not, but the story has been repeated in the United States for at least 89 years. I have a 1924 reprint of a book first published in 1912, Bert Wilson, Wireless Operator, by J. W. Duffield, and it includes the following:
Although this book is fiction, overall it seems to be accurate in its various accounts.