"""flowing over the top of the wing flows faster than air flowing underneath, which generates lift."
I do wish people would stop saying this. Aeroplanes, especially fighter jets, can fly upside down."
That is literally what happens, what doesn't happen is the production of a big enough pressure differential to lift the airframe. What actually happens* is that the air over the top flows faster than the air underneath and gets to the rear of the wing first, this then causes a downward flow of air at the trailing edge the mass of which is the same or greater than that of the aircraft causing an equal and opposite reaction and hence lift. Flip upside down and the same thing happens just with a equal** or lesser level of efficiency due to the shape of the wing.
*According to NASA, most pilot's licence exams still require the wrong answer.
**Assuming a symmetrical aerofoil.