Le Chaud Lapin writes:

This true and not true. A wing does not necessarily have to push air
downward to cause lift.

Not correct. Air (or some other mass) must be accelerated downward in order
to produce the upward acceleration of lift. There is no way around this. And
so wings must accelerate air downward in order to produce lift.

An airplane can stay aloft if rarefication is somehow created above
the wing. This is what's happening with the blow-over-paper trick.

An airplane can stay aloft by accelerating something downward (typically air).
No rarefaction is required.

Note that, in the paper trick, the airspeed of the paper is 0, and,
for all practical purpurposes, the air beneath the paper has no idea
that you're blowing on top of the wing.

Note also that the paper isn't doing any significant lifting.