You would not find American-trained doctors in El Valle de Anton and probably not even in the interior of the country (away from the Capital). The doctors in the Ministry of Health, which is the only clinic we have in El Valle, are probably trained in the University of Panama. The University of Panama had a well-regarded medical curriculum in the late '60s and early '70s and was sort of downgraded to train "country doctors." As far as I know, it is still that way now.
There might be American-trained doctors at the San Fernando Clinic, which is a fairly well-regarded clinic in Coronado, less than an hour away. In short, I can say that if you want somebody who is trained at the same level as how doctors are trained in the US, then you can go to San Fernando Clinic. And other than that, you may go to Panama City (less than 3 hours away) if that’s the level of care you think you need.
The doctors in El Valle are not altogether incompetent. Most of them are just not trained to a level they would have been trained if they were in the States. Most people in the United States think of medical education to consist of four years of pre-med, four years of med school, a year’s internship and a residency of three to four years at whatever specialty one wants to have. In Latin America, medical education normally consists of five or six years of medical school, followed by internships of two years. And then they will go into a residency which is probably three or four years depending on their specialty. Some of the doctors here are trained in Mexico.