This has happened to you or somebody you know?
As I had it explained to me one time when this rule first came into effect (2003'ish??) was that there were people who simply shot deer and then later on "discovered" the dead deer and were keeping the antlers.
I was miffed by the rule because it immediately made just about every deer mount in the state open to confiscation. Since then I have put my tag on the back of the plaque for all my mounts.
As far as I know, the State has not changed this part of the law. Nor do I know anyone who has run afoul of this and needed to challenge it.
From NDGF's website:
Permit Required to Possess Dead Deer
Mon, 10/31/2016
North Dakota Game and Fish Department enforcement personnel are issuing a reminder that a permit is required before taking possession of a dead deer, or any part of a dead deer such as a skull and antlers, found near a road or in a field. Only shed antlers can be possessed without a permit.
Permits to possess are free and available from game wardens and local law enforcement offices.
In addition, hunters are reminded to properly dispose of dead deer. Harvested deer cannot be left on the side of a roadway or in a ditch, and deer parts cannot be discarded in commercial dumpsters.