i am commenting in general - not regarding the doctors - in reponse to spl. my understanding is that a non-belizean resident can only obtain a permit to do business if they OWN the business, or it is a business /job that a belizean is incapable of doing.
this is to protect belizeans, and i (tho i don't live there) see the point.
there is always the possibility that gringo transplants who can afford possible higher rates would prefer a gringo dr, but that's a stretch. i do not know of anyone over the years who had a bad experience with the local doctors, tho i'm sure people cannot be 100% satisfied in every case.