Super, challenging question!
Both principles are correct, complementing one another.
Bernouli effect causes higher pressure under foil, lower above -- differential acting on foil area pushes up on airfoil, creating lift.
By Newton's 2nd law, the airfoil pushes down on the air around it with force equal to lift. If you map the air pressure below the foil, you will see a distribution of higher to lower pressure from the foil down to the ground. As you move away from the airfoil, the pressure decreases and spreads out in area. At ground level, there is a slight pressure rise above ambient (ie, ambient being any point far from the airfoil) covering a very large area. Integrating pressure x area over the ground yields the lift generated by the foil! (It's not really that surprising, is it?) That means that the ground is pushing up against the air, ie supporting the air, which is supporting the airfoil.
So good-old Newton is vindicated again.
I seem to remember solving this problem in aero engineering class in 1970 or so. Maybe one day I will try to find those notes.
"In God we trust, everyone else bring data"