I think there might be a case of running out of fuel here.
PA28-161 has useable 40 Imp Galls, uses 8 IG per hr and the distance from KTMB to MBPV is 500NM, at 100kts air speed, elapsed time is 5hrs and endurance 5 hrs!! This is assuming a direct flight and still air.
When I last flew on that route there was normally a headwind on the leg thru the Bahamas to Turks and Caicos.
Seems they were pushing their luck but got away with it.