I received a photo of a pile of toilet paper that had resulted from a toddler repeatedly hitting the roll and causing it to spill off. I gave the same advice that I give to other parents and pet owners, turn the roll around. I know that it is popular to say the toilet paper should go over the top of the roll. My suspicion is that it is funded by the toilet paper companies.
If the paper goes next to the wall, the pet or offspring needs to swipe up and this is a much less intuitive movement. Also, the paper is less likely to come into contact with the leg of a larger, possibly quite hairy, person. Keeping it next to the wall minimized the chances of that as well.