Sort of, the supply of physicians is artificially limited by the AMA - which dictates how many physicians there are. That keeps the cost of physicians nice and high.
100% agree but note that the AMA's limits are at a national level. So the [very high] base salaries are indeed driven by scarcity (as dictated by medical boards.) However the local scarcity is not driven by the AMA (note the salaries just get even higher! in remote locales as the local scarcity compounds atop national scarcity.)