There isn't a mountain in the Splash Mountain ride, either. In the original movie, it's just a pretty low hill and called "Chickapin Hill."
'Hill,' that is, not mountain.
And the outside is mostly just a giant briar patch.
Just because it was named "mountain" buy a Disney exec doesn't make it one. And the actual height of the attraction is not mountainous, either.
And the backstory in the queue contains a ridiculous etymology for it being called "Splash Mountain" (and an etiology for the rivers in the hill):
A backstory explaining how Chickapin Hill became flooded can be seen in a "Rabbit Tales" newspaper story in the queue:
Towering up and above everything hereabouts is Splash Mountain. Used to be that once upon a time, when most of us were still critlins, Splash Mountain was called Chick-A-Pin Hill. But that was then and back before a moonshining raccoon named Rackety, made a slight, but potent error. While mixing an experimental batch of brew, his juice producing still ended up being blown sky high. Many who were there at the time speculated that it was an overabundance of blueberries that caused the disaster.
This was unfortunate, not only for Rackety, but for the industrious Beaver Brothers, who had only recently finished construction on their new dam. Unknown to the Beaver Brothers, Rackety had built his juice still in the woods that backed up to their dam at the high end of the foothills. When the still exploded, the beaver dam burst forth, and all the water is was holding back, flooded the thousands of burrows, holes and tunnels that crisscrossed the inside of Chick-A-Pin Hill. From that time on, all the critters round here couldn't help but call this place Splash Mountain.
The revamped ride with PatF doesn't need to call it a mountain. And just like the big drop is representative of being thrown into a briar patch, and not an actual waterfall, so, too, the drop in Tiana's ride can represent something other than a waterfall, for example, riding the cresting waters of a breached levee.
