Very well said, bionic. With pets, the under-roll prevents them from unwinding the whole roll. My dogs do the same thing.
And by the way, pet-factor not included, simple physics will tell you that the under-roll or the over-roll makes no difference whatsoever as far as toilet paper unrolling on to the floor. Unless you have some kind of dispenser that has a gear-lock mechanism that prevents it from unrolling in the other direction... which would make you a point-one-percenter with no right to complain about anything.
The only advantage of the over roll is the ease of access. It's really not that big of a deal, unless someone has major OCD. I obsess about certain minor things myself. Proper care of milk cartons and condiment dispensers, proper loading of a dishwasher... and other things. Toilet paper? Nah, not at the top of my list.