It's a Cottonmouth Moccasin, not a rattlesnake. (There ARE several species of rattlesnake common in Florida, but if it was a Cottonmouth it wasn't a rattlesnake.) It's a very likely story, especially if he was near the edge of a body of water or a low marshy area, as these are water snakes that are not averse to venturing onto land.
They are not friendly snakes, and their venom is quite potent, but as a PP noted, hospitals in Florida are always well-equipped to deal with these bites, so if you get medical attention quickly, you'll almost always make a full recovery. Most Cottonmouth fatalities are to marsh hunters who are out alone and have to try to walk for miles to get to get back to a road and call for help.
Cottonmouths tend NOT to run away if you disturb them; they will turn toward you and bite if you get within range, though they won't chase you down if you back away from them. That old saw about the snakes being more afraid of you than you are of them isn't fully true with Cottonmouths; they are nasty-tempered little buggers.
When my brother was about 10, he and a friend decided to explore a creek bed when the water was all but gone; he saw an old door lying in the mud and like an idiot decided to lift it up and look underneath. What he found was an entire nest of Cottonmouths, and he just froze. The friend went runnning for my Dad, who by some miracle was able to get back with a loaded rifle before my brother got bitten. Dad counted 14 snakes after he shot them all.