Supposedly Disney routinely removes gators from the lake, but not "recently." Perhaps due to cost cutting? They have cut jobs recently from what I've read. I can't think that they won't be liable in some way. A no swimming sign seems harmless compared to a "beware of alligators" sign.
They'll be liable no matter what sign or fence they had up. That's just the way it is.
According to the FWC guy, they only remove alligators that are a nuisance. Probably like the golf courses do. And those gators are killed, they aren't moved.