Which is in St Andrews Bay. There are about 20 Alligator Points, he was at the one in St. Andrews Bay. Willow the authority on the region already confirmed he swam at Alligator Point in St Andrews Bay.
How do I know which Alligator Point he went swimming at? The one you are pointing me to is not in what I would call a bay, nor is it in the Gulf. It is actually part of a lagoon, even if the barrier beach has been breached.
The one I found just a few miles east is part of a bay, and is part of a larger bay. Both of them are fed by rivers, which tells me that they are not part of the ocean, the ocean spills into the river basin. This happens wherever a river flows into the ocean, and these areas are generally considered part of the river, not the ocean. Why is it different here? Is it because Obama is saying he swam in the Gulf?