My head hurts after reading other 'experts' and the link you provided in p
Many US patented airfoils have curved upper and lower surfaces, with the general airfoil having a more pronounced upper surface camber.
The expert's hypothesis (from the link from post # 3 'NPR's Lift') is that because airshow pilots fly upside down we should be suspicious of Bernoulli's Principle (BP).
In the same light, other 'experts' dismiss BP because a rubber band powered, flat-winged balsa wing airplane flies just fine.
Both theory of flight gurus seem to forget about angle of attack.
At increasing angles of attack, the relative lower pressure deepens until flow separation.
The balsa wood rubber band airplane's fuselage wing slot is angled up (positive angle of attack) with respect to the relative wind created while it's propeller pulls it through the air.
The flat wing is an airfoil, just not a very efficient one.
If the airshow pilot's plane does not have a symmetrical airfoil, he/she must fly at a greater angle of attack* when inverted than right side up at a given airspeed to maintain level flight.
I'm not ready to 'diss' BP. Think about all the naca airfoil patent paperwork nightmare that would ensue.
* when inverted pushing the nose higher above the horizon.
ps- I just didn't want anybody to attempt a split S close to the ground.