I agree it was irresponsible, but keep in mind these people were from Nebraska. Yes, everyone is aware of alligators, but if you're not from Florida, you don't really appreciate how common they are. They were probably thinking of them like bears. Every time we go to a park in north Georgia, there's theoretically bears there. But they aren't all that commonly seen, and I wouldn't think twice about letting my kid run up a trail 100 feet ahead of me. I think that's how people not from Florida think about alligators, not that they can literally be anywhere with water.
The signs should really say "Alligator Area - Stay Out". "No Swimming" probably isn't strong enough to keep someone from letting their kid put his feet in the water, or walk close to the water.
That said, given the amount of people that come through there without incident, this is really just the equivalent of a horrible accident, without a real need to place blame on either Disney or the parents. It's just a bad thing that happened.