Whatever it was related to, I would think it would apply equally to wild rats scurrying around where the guests will be. They are constantly throwing confetti, streamers, etc., in the parks that kids pick up off the ground. Also, a dead rodent in a guest room?- Whatever they were worried about in the show- I would think it would apply to guest rooms as well.
Actually, I suspect the rules at the show have less to do with Disney's particular concerns for the health of their guests, than they do with the strict regulations that typically surround the licensing of animal entertainment shows.
Disney could be in for some serious legal trouble, if they don't follow the state regulations to the letter. And the last they want is to get shut down, because they let a kid grab a leaf from the stage and someone tattled on them to the local authorities.
A rodent in the guest rooms? As long as Disney is following/exceeding the standards for cleanliness at a resort, there's no reason for them to worry. Rats happen.
The guest, on the other hand, is perfectly in their rights to request a different room.
And if you're freaked out thinking about it... Have you ever parked your butt on a grassy lawn? Thought your kids were cute, rolling down a hill? Gone for a hike in the woods? Everything you touch has also been touched by an animal or insect, and the odds are good it's been pooped, peed or sprayed on in one way or another. (I think about this every time I pick up after my dog, and then see kids drawing in chalk on the same sidewalk not an hour later.

)
Not to mention, rats are actually cleaner than squirrels.