I believe the attacker still gets to choose his loses in what you refer to as fly overs.
In the case of a flyover battle with an AA gun, the attacker could choose casualties but there isn’t much point. The reason being that you can only have a single air unit involved in the flyover battle as per rule #5 I stated above (i.e. one combat move). That means only one type of unit (either a fighter or a bomber) is present so there isn’t much point in choosing casualties.
I think this is an exception to the general rule that the opposing force always chooses their casualties.