Too lazy to quote the sites, but this is what I stated.
@El-Rami referenced military residencies for the OP as a way to make the Caribbean more palatable. Only people doing HPSP or USUHS would be eligible for this, not someone getting loan repayment from the military when they enter as a doctor (ie AFTER completing a residency).
Now someone could have the post 9/11 GI bill or even vocational rehab pay for a Caribbean school (post 9/11 would likely not cover tuition in full), but that would not make them eligible for a military residency either. Those are VA programs, not through the DOD. There is no service obligation afterwards attached to them.