To add another anecdote to this... not specific to the ship's medical. My spouse got the bends while diving in Belize. The dive center she was staying at tried to tell her she had the flu; she had to be emergency evacuated to the mainland by helicopter, and spent the next three days being treated in a bariatric chamber. Her travel buddy had to find lodging on her own. The bill for the helicopter alone was $15,000 and quickly appeared on our credit card.
The insurance eventually paid for all of it; she had substantial coverage. Coverage through her DAN membership plus travel insurance plus primary medical.
Everything had to be filed in order. Primary insurance first. They negotiated a lot down, but a lot was left on deductible. DAN insurance second, took care of most of the rest. Travel insurance last, they paid on the lodging and some of the helicopter.
But it took months, and it's not simply bureaucracy. A lot of money and proof of loss is required. You have to be patient.