South Texas rivers are often dry most of the year due to the Edwards Aquifer sequestering water underground. The ancient river system preserved within the Uvalde Gravel was probably similar, meaning animal remains had much less of a chance for getting buried. While the countless rounded stones of the formation indicate moving water, they do not necessarily suggest a constant presence.

I think the best shot for Pliocene fossils would theoretically have to either come from a flash flood deposit or possibly a spring fed pool deposit that stayed wet year-round (these are present sporadically in the Frio River today).

It's neat that even a lack of fossils can help to build an image of a prehistoric environment.