The last time my family and I were at Disney World was back in either 2009 or 2010. We stayed at a little boutique hotel in Celebration, FL, and visited the Town Center there, which is built around a nice lake. My two daughters were 3 and 4 (or 4 and 5) at the time, and we went for a twilight walk around the lake. There were numerous signs about alligators...but they weren't warning signs, IIRC, but signs stating it was against Florida law to antagonize the alligators. I kept a close eye on my kids, keeping them near me and away from the water, and staying on the paved path. There were other paths leading into the wilderness, but I wasn't going to take my kids on them at twilight.
I really feel for the parents. No parent wants to lose their child, but it must be horrendous to witness their child snatched away and to never see them again. Maybe I'm weird, but I've actually had nightmares where I've "dreamt" that I've witness one of my daughters was snatched by an alligator in front of me. Again, I don't want to minimize any parents loss, but if one's child was sick and passed due to illness, at least you'd have time with that child at the hospital, home, etc.
As for Disney, well I believe I read that this was a man made lake, am I sure they didn't purposely allow alligators in the lake, but any wildlife will find their way to the habitat of their choosing.
Authorities have already caught four alligators, euthanized them, and cut up their stomachs to see if they can find human remains, but no "success" yet.
Just a sad story all around.