The “happiest, safest, friendliest place on earth” isn’t going to spoil their image with “beware of the alligators” sign on a family friendly beach next to a child’s playground. This advertising, alone, is enough for a parent to feel they can walk with their child in a foot of water, safely, without their child being attacked by an alligator.
Normally it would be safe, and I think Disney has a fantastic track record in this regard. Families probably have thousands of times more risk of dying in car wrecks traveling to/from vacations like this.