The ‘corrected’ explanation is still wrong, of course—after all, how would the air going over the wing know how fast to go in order to meet up with the right ‘packet’ of air that went below? How would stuntplanes fly upside down? Hell, how could paper airplanes stay aloft?
In fact, wing shape has little to do with how planes fly; in the end, it’s all just Newton’s third law: air goes down, plane goes up. (For more explanation, see e.g. here.)
Which is complicated by the fact that they do use the Bernoulli effect, but that doesn’t mean what most people think it means. The Bernoulli effect is actually just the statement of Newton’s second law in a fluid context, rather than in the discrete-objects context where it’s usually discussed.
Bernoulli is fine actually. So is Newton. They are different ways of measuring the same thing. What is missing is that wing curvature is not the only thing that accelerates the air mass.
Well, I’m more intrigued by how the Bernouilli Effect can act on paper sheets lying flat in a photocopier tray. If you’re just having a tube that lowers the pressure on the top side of the paper, that’s a sucker, not an airfoil.