They say it's incorrect because it doesnt account for the airflow on the top. Well the flow on the top doesnt strike the wing (except its forward facing part, the wing is pitched 'up' slightly) so it doesnt push it down. But the bottom flow does push it up (it strikes the whole surface of the wing).
Really cant see whats wrong with this simple explanation.
The flow above the airfoil "sticks" to the airfoil. Since the upper flow is being forced downwards by the curved upper surface, it forces the airfoil to move upwards.
What happens if the upper flow doesn't curve downwards? Simple. That's called "stall," and your airplane drops out of the sky. "Stall" is when the upper flow becomes detached, and goes straight back, rather than following the curved upper surface. (The force on the bottom of the airfoil is far too small to keep the plane in the air. Most of the lift is created by the upper surface! That's why "stall" is such a huge deal.)
But the simple explanation is wrong because when you actually do the sums the numbers don't add up ... there is more going on.
So it's more complicated than that.
Downwash (in the context of lift generating wings) refers to the downwards motions of air generated by tip vortices (look-up "induced drag" for more details). This is not the same as the net downwards motion of the air in the wake, relative to the free-stream air. Take for example, an infinite wing (or a 2D wing). Here, there is no downwash but we still generate lift and have a net downwards motion of the air in the wake. You can see this with online fluid simulators for airfoil sections, many of them are 2D.