I put mine under on account of my cats just loooove spinning the roll like crazy. If I put it over the top, I come home to piles of shredded TP in every bathroom.
We had a (late, lamented) cat that did that. Unfortunately, putting the roll under just meant we got clawed up rolls of toilet paper, rather than rolls of usable, but unraveled, TP. He was a stubborn little bugger. We ended up having to take the TP off the roll and put it on top of the toilet tank until he found another hobby.