The aerofoil (or for what matters the entire airframe) doesn't know what's up and what's down as long as the entire contraption is flown straight and lever at constant speed
True- but what is missing from this ' erudite' discussion is the concept of up versus down.
For a standard airfoil - it is shaped such that the ( lift vector ) in normal flight is UP which allows the plane to fly level and generally at right angles to the gravity vector ( DOWN ) in normal flight. When the two vectors ( lift versus gravity or UP versus DOWN ) balance- the plane flys level at some elevation above local earth.
BUT if you turn the same wing inverted or upside down , then the LIFT VECTOR ADDS TO THE GRAVITY VECTOR, and absent some other forces the plane will go down, still in level flight -at least for a while.
Keep in mind that I am talking steady state conditions- absent any other control manipulations or forward vector changes in speed- momentum which can delay the result net DOWN for a while.