Ok, this has been brought up a few times, and there seems to be a common misunderstanding here, so here's my input:
The reason you shouldn't release a bow from full draw without an arrow is that the potential energy that should have propelled the arrow now has nowhere to go apart from back into the bow. And since the bow is being braced by your hand, this sends a shock through it that can cause it to break.
EXCEPT that's not what's happening here, because I'm holding the bow the other way around. So the energy that would have propelled the arrow is now propelling the bow itself. And since the bow is significantly heavier than an arrow, that energy can all be safely converted to kinetic energy (and then the bow is stopped by an impact with a pliable surface, which deals with any excess momentum)
Of course, there are a myriad reasons why this is inadvisable, but it's not actually the same as dry-firing the bow!