I agree with APD.
The problem isn't necessarily any problem with the students down there (although there are some who probably shouldn't be in med school, a lot of those probably flunk out before getting to the residency-application point). The problem is with some of the schools down there; it just takes tremendous resources to properly educate a medical student. There needs to be some 1-on-1 teaching in an appropriate hospital setting. There needs to be a curriculum that is not haphazard, that is well set up. There needs to be competent instructors who are up on the latest research/info from their fields. I could go on and on, but it's just hard to understand and appreciate if you're a premed student.
Also, in truth some of the Caribbean schools (and some DO schools, historially, though not as much so now) take students who could not make the cut at US schools, academically. Some of those schools will take just about anyone, and then they don't do much to educate them. The people, if motivated and reasonably smart, can memorize or learn enough stuff to pass the US medical licensing exam that will allow them to apply for a US residency. However, some of them didn't get taught how to properly approach thinking about a sick patient, and/or how to examine a patient, and how to work in a US hospital effectively. You can't just learn to be a doctor from reading a book (or books).
Yes, some of it is probably just "name brand bias" from program directors, but there are just a lot of reasons why they don't prefer Caribbean grads. That doesn't mean there aren't a lot of individual good Caribbean students or a couple schools down there that are probably pretty good, but there are a lot of crappy ones. All you have to do is to do a Google search to find that out.
Also, historically (and I guess maybe presently too?) there have been students who went to the Caribbean and graduated after being kicked out of US schools for some sort of misbehavior like cheating, etc. Also there may be people who had some sort of criminal conviction, etc. I think these people are probably pretty rare, but some med school faculty members are leery of stuff like this.