Not being from FL, if I see a sign that simply says "No swimming" I'm thinking, in the water up to your chest kind of no swimming. Letting my toddler splash around in very shallow water is not swimming to me, therefore I wouldn't be 'ignoring' the signs. Even riptides can't grab you unless the water is at least knee deep.
If I saw a sign that said, "WARNING, ALLIGATORS" I'd be a LOT more weary about letting my toddler play.
And while yes, Commin sense says there are gators in FL, I would've thought Disney would take precautions to keep them away (Gates at the waterway openings, etc) and I would not necessarily be thinking I needed to watch for them at my Disney owned resort. Not that they are responsible I'm not saying that, I'm just saying I would not have thought of that if I wasn't living there.
I agree with all of that except for the very last bit. I am frankly amazed that Disney built those hotels, built the waterways and put those beaches there without being sure they could keep away gators. I remember being at the Poly and being told by staff we could splash in the lagoon but no swimming. We still didn't go in at all but that's what we were told and no sign or person ever mentioned gators. I always assumed that Disney built all this this way because they were confident the area could be kept gator free. Imho this is a massive fail on Disney's part.