The logic being:
The AA Gun was technically involved in a Combat (even if it did not fire at planes during the combat), so it cannot make a Non-combat move. The only pieces that defy this general rule are planes (explicitly excepted in the rulebook) and Panzerblitzing German tanks (German National Advantage - also explicitly excepted.)
This might also be explained as a common behaviour of the grey pieces - AA Guns and Complexes - in that if they are captured or liberated, the new owner doesn’t assume functional control of them until the end of the turn during which their capture or liberation occurred. I actually like this justification better than the one above.
~Josh