Does flying an airplane upside down imply negative AoA? Why? I saw the statement below in this answer:


  Note that for normal level unaccelerated flight $C_L$ is always > 0. The minimum $C_L$ is a negative value for negative AoA, and would mean that the aeroplane is flying upside down.


This would seem to me to imply that flying an airplane upside down implies a negative angle of attack.

But the typical illustration and explanation of angle of attack is that it is the angle between the airstream and a reference line, the latter of which in airplanes is normally the wing chord.

How can the two be reconciled? Alternatively, what am I missing?
Level flight (no change in altitude) upside down, with an airfoil with a zero-lift AoA of less than or equal to zero degrees, requires a negative AoA to get upwards lift. 

This is assuming the AoA is measured in the body frame of the aircraft, aligned with the chord line of the airfoil.

Also this assumes there is no thrust/drag or thrust/drag do not meaningfully contribute to vertical net forces.