Okay, let's try this approach. Some of you are still not understanding the *concept* of spell types.
Enchantment-Compulsion: The spell forces the subject to act in some manner or changes the way her mind works. Some spells determine the subject's actions (or the effects on the subject), some allow you to determine the subject's actions when you cast the spell and others give you ongoing control over the subject.
While discussing whether or not Fly is controlled through a mental action, you are completely forgetting about the Hold spell itself. Hold spells *Compel* the target, through enchantment to NOT move. The target thinks, "Hey, I can just coast along with my fly spell.", but the Hold Person spell, being and Echantment-compulsion, magically causes the target to think, "No, I will just stay here and do nothing." Whether Fly is controlled by mental action is moot. IF (big IF) Hold person was a transmutation or abjuration spell that held the target (via a force field) for example, then you would be able to still Fly with the spell. But the Hold person spell is a Compulsion that is compelling the target to not move.