This is a rule for pretty much any disc player that doesn't require you to snap the disc onto the spindle (think Walkman CD players, PS2 Slims, or laptops). The sticker is there as an idiot-warning because people are screaming for doing dumb stuff like moving their consoles while they're on. Now if you move it very very slowly, you can get away with it, but you have to be super-careful.
Rather than have people whining about their borked copies of Hello Kitty Island Adventure, apparently Microsoft thought it was a good idea to use the sticker instead. This seems to have backfired.
Of course they could have used the snap-spindle design, but this requires access to a lot of inner console surface area (great for kids with food, pocket change, etc) or the design used in laptops, both of which would sacrifice precious reliability. A sticker is bad press for a little while, hosed drives are worse.