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It gets a little complicated. The Bernoulli Effect is real and is what is being portrayed in the lift distribution models on airfoils. This effect, airfoil shape, angle of attack and flow velocity all work together to accelerate the air mass downward at a sufficient rate to maintain the required lift to maintain the aircraft. As the aircraft gets close to the ground (ground effect) as in landing the trapped airflow pushes against the asphalt which doesn't give and creates more effective lift. Many a car has suffered troubles with more air-pressure under the car than over the top. That's why they have front air dams.
It has always been known that air displacement is the working effect. By the time you get done explaining Bernoulli effect most peoples eyes glaze over, so most books and instructors go for the simplist explanation.
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