Dave, Check your leg. Did you feel a tugging sensation as the guy was talking to you? I don't mean to negate the guy's message of caution entirely, but it was a bit over the top. There's been the occasional very small child of a northerner eaten by a gator, and little dogs get eaten all the time, but we have more problems like that with cougars in the Rocky Mountains than with gators here in Florida.
A couple years ago on a guided tour through some Florida swamps the guide said this about alligators: "Alligators are stupid animals. They understand only two things: predators and prey. They think people are predators and stay away from them until someone feeds them; then they think people are prey." And that's why in Florida "A fed gator is a dead gator." Once they've been fed they have to be killed. Which is not to say you don't have to be careful around them, but they aren't the hazard some locals will claim if you're a visitor. I suspect most of the people with those fences you mentioned have dogs.
Last year my wife was working in her garden behind our house, with her back to the pond (which has no fences) when, as she says, she "felt a presence." She turned around, and a five-foot gator (a small one) had come out of the pond behind her and was sunning himself on the bank. As soon as she turned around the gator got scared and flipped back into the pond. Nowadays she tends to work facing the pond.
Several years ago I was riding my road bike on a Florida back road. I was doing about 20mph as I came over a little hill, and right in front of me, on the left side of the road, was a gator. There was no way I could stop in time, but he was heading back to a pond off the right side of the road and I figured I could just roll past behind him. But as soon as he saw me he stopped cold. I had to roll by right in front of him, and he opened his mouth wide as I went by. But it's clear he was at least as scared of me as I was of him.
But my wife has an even hairier story from Colorado. She often walks in Garden of the Gods early in the morning. One morning she was coming across a parking lot near a local tourist attraction when, again, as she says, she "felt a presence." She turned around, and a large cougar was standing about fifteen feet away, staring at her. Fortunately, the cat had just eaten, because his mouth was all bloody. She raised her arms to make her look bigger and backed away slowly. The cat turned and slunk off. Nowadays she walks a bit later in the day.