Do the same experiment with the paper, but rest the trailing edge on a table. The air can no longer be deflected downwards, so the paper will not rise.

Another one to think about, at the air metal boundary the air is stationary on both sides of the wing. So why is there a pressure difference? Bernoulli's law is valid only along flow lines and is a consequence pressure difference required to accelerate (or decelerate) a fluid. Since in the laminar situation flow does not occur from the top surface to the bottom (minus around the tips), direct application is nonsensical. If you integrated all flow lines from all surfaces however, you would get the correct answer.