Well.. technically you could, though it would probably be immoral. Other than that, you probably could.

Paper's one true weakness - Rustling. Scissors can get rusty and rocks can corrode, crumble, and more. They can all blunder in one way or another; it's wonder that people usually never think of these when playing the game.

The early bird catches the worm! ;)

The silent lion claims the prey! ;)

Hmmm, perhaps. But then again, couldn't rock do that to paper? 0_0

Yes, supposedly Paper "magically" wraps itself around the rock. What happens beyond this point is unmentioned.

As far as I see it, immobility would be the only explanation, as Paper has no clear value to it rather than the fact that it is capable of more movement that the scissors or rock.

Perhaps the paper is meant to move vertically towards the opposing object; it would be moving straight into open scissors, and it would be able to sort of "mold" itself around the rock.

That's my viewpoint; that immobility is the only explanation.