St. Matthew's is a relatively new school in the Caribbean scene. It had a lot of problems when I first started at the school, namely due to bad management in addition to the newly formed school kinks that you'll see around.
Since then, they have changed administrations and moved to Cayman Islands. Since the move things have improved dramatically. We have on-line access to all our records (registrar, fin aid, etc) in addition to access to many journals. Other improvements have been more efficient service from the office regarding fin aid, rotation scheduling, and registration. I am now in clinicals so I don't directly know about the teaching but the word from others is that it is solid now compared to the early years.
My advice to you would be to try the US school, DO schools, SGU, Ross, or AUC. If those options (for whatever reason) do not pan out then St. Matthew's is a great option. I mention the other schools ahead of SMU because they have California & NY approval whereas SMU is in the approval process as we speak.
Best of Luck!