I'm surprised people don't start with the basics on this confusing topic. The third law of Newton's mechanics tells us that for the plane to get an up force to counteract the gravity, the air must receive and equal amount of down force. Therefore what planes must be doing is deflect air masses down. A plane must be applying a downward force to air masses, with total force value of "mass * g", i.e. supply "mass * g *…
In this case, you say simply that 'oh it's the equal and opposite reaction', and that seems theoretically possible. But then you do the experiment, and all of a sudden, you see not only a force due to the third law, but also a pressure differential. Based on the laws of pressure, a high pressure beneath the wing and a lower pressure on top must also exert a force. These pressure laws are as fundamental (and are actually simply a consequence of the third law, since pressure is just a statistical approximation of the third law applied to invisible microscopic particles).
Thus, while almost certainly true the third law does contribute, it's also true that it is not a full explanation. The third law could explain lift, but it does not explain why the pressure differential would exist, and thus cannot account for the extra lift due to that.
The third law would additionally predict that the pressure on top should be greater than that on the bottom. This is an easy experiment to do. Get a piston in a closed cylinder (the piston does not need to partition the cylinder). Place two pressure gauges on each side. Now pull the piston up. The side being compressed has higher pressure. This suggests that, if a flat board moves towards a side of a closed system, that side of the system ought to experience higher pressure. But it doesn't in the case of wings, so that's weird