Figure 1 illustrates a holder dating back to the dawn of scrolled toilet paper as we know it today. This type of device was a wooden cylinder held by a simple wire bail, which was attached to the wall (outdoor or indoor) with some sort of cleat or clamp. As Figure 1 shows, the overhand hanging method is most appropriate for one of these old-timey fixtures; the underhand method would leave the end sheet of the paper in a position to adhere to the wall via static cling (or indelicate residues), slightly complicating the task at hand for the user.
Figure 2, by contrast, shows a typical modern recessed fixture, which seems to be purpose-designed for the underhand hanging method; this design provides a "grasping margin" between wall and paper, owing to the paper's pseudo-cantilevering effect as it emerges from the recess and falls under the unconstrained influence of gravity. Using the overhand method with this type of modern fixture creates, psychologically, a more aggressive incursion into the bathroom's living space because the paper creates a sort of inverse knee-wall or short partition that gives the illusion of reducing potty elbow-room.And that, as legendary WGN morning man Wally Phillips used to say, is why we call this "The Learning Place."