That's true. It's really rare for one to pursue you past the initial lunge out of the water though. I've lived in FL all my life and I've never been concerned about alligators. A healthy respect for them and being aware of your surroundings should keep you safe. Residents of the state of Ohio, or as we like to call it down here, North Florida, can attest to the fact that a lack of respect for the Gator usually doesn't end well.
In regards to crocodiles, there are some in FL, however they are rare. I've personally never seen one in the wild. Crocodiles are probably more dangerous to humans than alligators, but it's unlikely you'll ever come in contact with one.
Regardless, the presence of alligators and crocodiles should in no way influence your decision of whether or not to live FL.
Maybe I'll get an alligator tattoo.....