A brick could fly with enough speed if it were inclined, just as a flat plate works, with enough q, of course.
Lift can be explained either with Bernoulli or via the Newton method (regardless of the fluid you are travelling through)
Bernoulli depends on Newton in various ways (such as continuity.
Newton's method depends on airflow being deflected by Bernoulli, so to get the amount of air deflected off the top of the wing you need you must have the pressure differences that are explained only by Bernoulli so the flow is forced around.
What is being missed here is that these are not conflicting theories at all. They are not even complimentary (meaning that you don't get "part of the lift" from one theory and "part" from another). They are just different ways of _quantifying_ the results. Either way you can come up with ALL the force you need. If you want to work harder you could do part and part I suppose, but that would be a bit silly.