I never play with a console vertically, except for my Wii, which loads everything off of my HDD (sitting horizontally).
A spinning disk pulls toward its axis, and if you switch axis while in motion, the constant motion will be broken, and the disk will come off the axis. I can't remember what the two types of motion were called,but either way, they are limited to the vertical axis and horizontal axis due to gravity. Therefore either one is a good as the other, but cannot be switched while in motion. I play the console it its most rigid position, pervy sounding, yes.
I have actually watched someone move their console from vert to horizontal b4, and it was hilarious! They completely destroyed their GH3 disk.
But, yeah. Anyone who says one way or the other is damaging has no common sense, or at least refuses to back their statements scientifically.