If you are asserting that the angle of attack does not affect the lift, you are wrong.
A plane flying upside down is most certainly not using the same angle of attack as it does right side up. The real difference in performance is efficiency, the upside down plane is burning more fuel due to the increased drag from sub-optimal operation (a high angle of attack to overcome the optimization for right-side-up flying).
Note that a right-side-up wing can easily plummet by dropping its angle of attack. That is what it's doing while upside down to generate lift.
A plane flying upside down is most certainly not using the same angle of attack as it does right side up. The real difference in performance is efficiency, the upside down plane is burning more fuel due to the increased drag from sub-optimal operation (a high angle of attack to overcome the optimization for right-side-up flying).
Note that a right-side-up wing can easily plummet by dropping its angle of attack. That is what it's doing while upside down to generate lift.