I've spent a frustrating two hours trying to animate and running into the same problem.
When I move a specific object in object mode, the armature doesn't move. When I put it into pose and move that object, the armature doesn't move. When I record an animation and move that object, the armature moves all over the shop, messing up everything attached to it.
I've cleared parent (I think) between the object and the armature, and between the armature and the object. (There should never have been a parent there).
Unless the problem is somewhere else, I think it might still be a parenting issue. How can I see what the parent is - other than with the very-un-clear dotted parent lines (of which there are too many in the scene anyway)?