Correct. Since Eagle Eye was not transferring possession, his interstate moves were moot from the standpoint of federal law.
It is perfectly legal for a person to move from one state to another and take all his firearms with him. Transferring ownership (whether via gift, purchase or trade) between two persons who do not reside in the same state is a different story. That requires the assistance of an FFL.
The only exception I'm aware of is that if a person dies they can leave their firearms to a resident of another state in their will and that transfer doesn't require an FFL.
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