FIrst off, notice that nowhere in NASA does it say it's "part Newton and part Bernoulli". Note that. There is something called impact lift, which does play a major factor at very high altitude hypersonic speeds, but is virtually negligible below that.
Now, the issue is between what you found on the NASA site. That is a nice engineering model, but it begs the question of "why". Nothing ever moves because it is "pulled", it is always pushed, this is basic Newtonian physics (which, of course, is just a rough model because it doesn't include relativisitic effects).
The air does stick to the surface, but what is actually causing the force itself. It is not Newton's third law. If you look at Newton's laws, they are all very intuitive, but often misapplied.
Bernoulli could be considered an adaption of Newton's laws also, for that matter. The Newton model you described is a nice model, but does not tell you "why". It is like the description of how swept wings reduce the effective mach number by dividing up the flow into vectors, one along the leading edge and the other perpendicular. Nice, you can make some calc's, but does not tell you WHY. Don't confuse models with how something really works.
Reading your excerpt again, I find it hard to believe that NASA would put that. The notion that the air above and below the wing have to "join" at the trailing edge is flat out wrong. In fact, the air across the top gets there well ahead of the air on the bottom.
As to your "the air hits the ground and pushes". Pushes against what? Do you think a balloon that you untie and let go flys around becase the air is "pushing" against the air it hits as it leaves the open end? Is that how rockets work, they "push" the air the exhaust hits (oops, they work in a vacuum too).
I do not mean this to sound harsh, but think about the actual physical process that's involved here, not a esoteric model that is nice to use to make these things opaque.