That page is arguing against a straw man. Nobody is claiming that the full dynamics of a wing are exactly that of a flat sheet at an angle (with full flow separation etc).

The point is that a flat plane with full flow separations is the minimum necessary physics to explain lift. It would obviously make a terrible wing, and it doesn't explain everything about how real wings are optimised. That's not the point.

In any case, I only said the wing pushes the air down. I didn't say it only uses its bottom surface to push the air down.