Counter point:
Pilot has a sick passenger. He's not sure how sick. He asks ATC about landing at JFK, to which he is told to call Port Authority. He disappears off frequency, comes back and asks about landing on the beach, then does.
What was he told when he called Port Authority? If its anything like "You can't land here," or "It will cost you a few thousand dollars to land here," and his passenger was, in fact, getting sicker by the moment, maybe he thought that was the best way to go.
Additionally, he was kept below 500ft. If he was, in fact, having engine trouble, I'm not sure that he could have made it to KJFK from where he was, if that's true.