I think you can have both even with supernatural reanimation.

Say an exterior force takes hold of the corpse and moves it. In that instance it's not being moved by the bodies own physical properties, but merely the force of whatever spirit has gripped it. Think puppetry or telekinetics.

On the other hand, an interior force would be bound by the bodies limits, like say a soul being forced back into a corpse. In this case, you could have slow and perpetually rotting zombies who are also self aware, which is all the more horrifying.