Jon,
That is one of the ways that Jamaica has been assisting with the British High Commission. I have not heard of any hotels holding guest at ransom as has been happening elsewhere.
When I got stranded here after Gilbert in '88, we were stuck for 5 days. No one charged for anything but we did offer token payments since there was no way to get cash. Hotels across the island did not charge for the extra days. When you are stressed out, that is worth more than money!