I am acquainted with, at least, one gentleman who attended a foreign medical school (Dominican Republic). The lack of name-brand credentials has not dampened his style or career in the least.
There are many sensible reasons for an education maverick, who dreams of becoming a physician, to go to the Caribbean and study medicine, as this article points out. At the American University of the Caribbean in St. Maarten classes are in English, the tuition is cheaper than that of U.S. schools, and a bachelor's degree isn't required for admission.
Belize is another tiny nation with a medical program, although Central America Health Sciences University didn't make this reviewer's "strong players" list. But that's just one opinion.
St. Matthews in Grand Cayman (absolutely charming island!) even has a vet school.
Island hopping for an M.D. progam could be the ideal working vacation for an adventuresome soul.
There are many sensible reasons for an education maverick, who dreams of becoming a physician, to go to the Caribbean and study medicine, as this article points 