How medicine worked in the Middle Ages was more like mysticism and superstition than real science. Besides the case of Plague Doctor is special because it was more a mortician than a doctor. The theme of the purge and Extreme Unction seem to have much to do with the role of the priest. Put away the evil from patient and accompany him in death.
Taoism is not a religion but rather an occult science, such as alchemy. The Taoists were advising the upper classes of Chinese cities on morality and health. They predicted the future in the stars but mostly are the first scientists to catalog the reign of living. Of course they are related to the study of the five elements and ki.