And they're labelled as such.
A less-fuzzy example is the wolf/dog Trip special attack:
A wolf that hits with a bite attack can attempt to trip the opponent (+1 check modifier) as a free action without making a touch attack or provoking an attack of opportunity.
If you provoke an AoO, I can't hit you with my dagger, then cast a Quickened Magic Missile. It's not my turn, and free actions are taken during your turn, and an AoO is a single melee attack. The AoO doesn't allow me to work an extra free action in there.
Likewise, if you provoke an AoO, I can't drop my dagger, quickdraw my greatsword, and hit you with it.
Should a wolf, after making his single melee attack, be able to take an extra free action outside of his own turn to trip you... when the Trip text makes no provision for the free action to be available outside the normal turn sequence?
-Hyp.