Unless the Feat says so explicitly, the creature does provoke AoOs from movement.
Fly by Attack is actually a more generic version of Spring Attack and Shot on the Run. Sometimes SA is better, sometimes SotR is better, sometimes FbA is better.
FbA makes more sense for non-humanoids who may want to combine movement with a melee attack, a spell, a breathe weapon, or some other supernatural ability. In the case of, say, a Dragon Flyby is much better than Spring Attack even he it can result in an AoO under some circumstances.