How I hate that article. Poor John D. Anderson will forever be associated with this ridiculous claim that no one knows why aircraft fly. Also note, that he does not say that at all:

“What Anderson said, however, is that there is actually no agreement on what generates the aerodynamic force known as lift. “There is no simple one-liner answer to this,” he told the Times.

Not only does he not say that no one understands lift, he also doesn’t say that there is no agreement. What he says is that there is no simple answer. That means something completely differently.

Edit: there are two fundamental ways to describe lift: as the resulting force from integrating pressure over the surface of the wing (here discussed in a distorted way as ‘Bernoulli’), and a control volume way of Newton’s 3rd axiom, where air is pushed downwards by the wing and the wing in turn experienced a force in the opposite direction.

There is no mystery. Both views are equivalent. What is hard is to predict the exact force, as one would have to predict the flow field around the wing.