A Physician gets paid a physician's salary and performs the duties defined by their specific role or specialty(more often what their malpractice covers them for). To become a licensed physician you need either an MD or DO (in the US atleast, I guess for that matter you can have an MBBS or the other dozen medical degree and pass the USMLE and do a residency in the US to practice here). I recently read a statistic that 40% I belive of the physician in New Jersey are foreign medical graduates, many of these institutions do not grant an MD, they may have that on their white coat, but that is not their degree. So enough with the MD/DO, if your a physician your a physician and are granted all the priveledges thereunto pertaining.
The same thing if you want to be a dentist, you need either a DDS or a DMD. The same thing if you want to be a vet, you need either a VMD or a DVM. The same thing if you want to work at a bank, you can have a degree in finance, business, or who knows what else. The DO is your degree, not the title of your job. A chemical engineer is a chemical engineer, they aren't refered to by BS or a MS.