I am not saying it cannot make sense I just wanted to clarify. It was given the nickname splash mountain in story and before that in marketing the same way Space Mountain is a nickname that started it all. It is all the art of naming. The same way Big Thunder Mountain is a nickname given by the locals because it rolls thunderous sounds from explosions and earthquakes, not because it is thunder. Splash Mountain is the ride's name because of the critter's naming the infamous chickapin hill.
To your other point. Ga has, Stone Mountian and large rolling hills.
Stone Mountain isn't really a mountain (it's just a giant rock), but northern Georgia does have actual mountains (which are much bigger than Stone Mountain). Louisiana doesn't really have any mountains.
Regardless, the Brer stories don't take place in the Georgia mountains, so it's a moot point.