Hmm... I'm certainly rusty on physics principles, but as far as I remember the (flawed) classic bernoulli effect explanation of airfoil (assume equal travel time ... pressure differential causes lift) does not really directly talk about moving air down at all, and would hypothetically still work if all downward air movement from the top of the wing were magically canceled out, (and airfoil had an attitude of 0 degrees, so no downward air movement from the bottom).
Now granted even with that magic, there would be downward air movement relative to the airfoil, due to the airfoil rising, but that would be an effect of the lift, not a cause.
Now I could well be overlooking something here, and having invoked magic to violate conservation of momentum, this thought experiment is not rigorous, and is discounting the fact that the equal time hypothesis is unfounded, and even wrong. (But in reality the air above moves faster, so we would see a larger effect than predicted, even before accounting for redirected airflow.)
Of course there is no magic canceling out any downward momentum of the air from the top of the wing, and planes normally have a nose up attitude, so the bottom of the wing also directly reflects air downward, so downward directed airflow is definately also a cause of lift.
Now granted even with that magic, there would be downward air movement relative to the airfoil, due to the airfoil rising, but that would be an effect of the lift, not a cause.
Now I could well be overlooking something here, and having invoked magic to violate conservation of momentum, this thought experiment is not rigorous, and is discounting the fact that the equal time hypothesis is unfounded, and even wrong. (But in reality the air above moves faster, so we would see a larger effect than predicted, even before accounting for redirected airflow.)
Of course there is no magic canceling out any downward momentum of the air from the top of the wing, and planes normally have a nose up attitude, so the bottom of the wing also directly reflects air downward, so downward directed airflow is definately also a cause of lift.