You're conveniently ignoring drag which would make it impossible to stay in once place as you suggest

Very obviously faked. Assuming for a minute that the wing on the paper airplane is actually a wing, lift will be created by air passing over the wing, which will keep the plane in the air. However, it will also create drag which will create a force pushing the plane backwards. This video would have you believe that the other fan is opposing this drag force by blowing in the opposite direction. However to create an equal force of, and have the plane stay in one place, the air speed from behind would have to equal the air speed from the front, which would create effectively zero airspeed at the wing, causing it to have no lift, and of course fall to the ground :)

Actually, water is incredibly good at stopping radiation....so maybe its not such a bad idea ;P