the left hand seat pilot is fully legal to be flying solo - it is simply being done to keep the insurers happy.
If Insurance is mandatory in Barbados then it would not be legal if the insurers had not agreed to insure this pilot.
all are required to have a checkout by a CFI
A checkout implies that the person being checked is under some form of review which then poses the question, what if the reviewer is not happy with the performance of the person he is reviewing. If the reviewer were not PIC i.e responsible for the flight then they would not be able take control should it prove necessary.
By insisting that an instructor conduct such a flight, the insurer is reliant on that persons experience and integrity to do the job properly. If they are banned from operating in local airspace then should your aircraft be involved in an accident, it is highly unlikely that the insurers would pay you a penny.