A surgeon's inheritance alone counts for little when it comes to evaluating his or her medical expertise. If it did, Chinese bartenders would be more skilled at Asian plastic surgery than American super-specialists.
While many patients simply assume that, for instance, a plastic surgeon of Korean ethnicity must have a better feel for Asian aesthetics and what a patient wants or needs, there seems to be little correlation between surgical outcome and a doctor's racial background, especially with cosmetic surgeons practicing outside of East Asia.
When a doctor has been educated in the West or is simply the offspring of immigrant grandparents or parents to a Western country, he or she may be more "Asian" in name than anything else.
The other selection factors noted to the below matter much more than surgeon ethnicty.