I'm not saying there's NEVER been Gators at Uni, it's just MUCH more rare than at Disney, where, if you're actually paying attention, you'll see them almost every day near the waters, sun bathing on the golf courses, on the side of the road, etc.
And yes, since there's so many Gators in the state, the FWC has stated that Disney has no choice but to kill the gators. There's nowhere they can be moved.