I have my stance because I know where I am going, without anyone warning me. I don't know about every harmful thing at every place, I'm not saying that I extensively research all wildlife of where I am travelling, but I just do not think about the probability of an attack.
If I did then I would never do another dive or take my kid snorkeling...I just don't want to think about those things. Yes, I'm aware of my surroundings, I do night dives but I won't take my son in the ocean at night. I stay away from grassy areas in bodies of water etc. But I don't walk around thinking an attack will happen.
I have no knowledge of the ground at Shades of Green, but from what you described there is a very good reason for the signs. Water and grass off of a sidewalk are awesome areas for alligators. A beach full of people during a movie is not. An attack at either place would have been shocking, the GF beach, more shocking, because no one expects for an alligator to come around with that many people there.