Bottom line: Just be informed and careful around gators.
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Absolutely correct. Like most long time Floridians I have my own natural fear of gators but on the other hand I'm not paranoid around them. My rule is that: if you go swimming in fresh water in Florida then you are swimming with gators. You just won't see them most of the time. I don't go in the water near dawn or near dusk when visibility is poor. Or after dark. And that applies to salt water because of sharks.
There is another park with seemly fearless gators, Myakka River SP. That lake is full of gators and in this case they are being fed with the apparent approval of the park rangers. They have a non-native fish problem and there are a lot of fishermen near a dam on the lake. They catch the worthless non native fish and kill them, at the end of day they throw them back into the water and the gators are there waiting.