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.
Not sure why people are looking at the situation as ONE Venturi plane. What I am trying to explain is that there is effectively TWO - and expanding one over the top of the wing leading to a low pressure effect, and a constricting one below the wing leading to a high pressure situation. I wouldn't say that both provide equal amounts of lift, but the paper experiment, and the 747 in the boneyard proves it to a point.
Extend the flaps and slats on that aircraft and I am sure the effect will be all the more pronounced.
And yes I've flown aircraft inverted too - it take a tremendous amount of forward stick to try and maintain level flight in that config to counteract the wings natural tendency to move towards the top surface.
People have pointed out the "Thunderbirds" F-16s flying in the "mirror" formation [1] and not displaying much difference in AoA between the upright and inverted aircraft, but supersonic fighter usually have a straighter, almost trapezoidal shaped wing cross section rather than a curved 'fish' shape. I am willing to bet the inverted pilot has a fair bit of forward stick on though.
[0] - https://www.youtube.com/watch?v=cHhZwvdRR5c
[1] - http://c8.alamy.com/comp/EG175E/little-rock-air-force-base-a...
No one questions whether the Bernoulli and Venturi effects actually exist. But airplanes are heavy and it's pretty obvious that the Bernoulli effect does not produce sufficient lift by itself.
As proof that most of the lift comes from deflecting air, I offer the fact that airplanes can fly upside down.