SNS3, there is no suggestion that the frigate concerned was in the ADIZ or in fact anywhere near. All hardhatter wrote was:
The frigate was lying in green water, escorting a human-aid transport ship.
Now I don't know the exact location of the ADIZ but I don't think the ADIZ is anywhere near where a human-aid transport ship would need an escort from a warship. That would be more appropriate for places like Iraq or Somalia, not Washington DC.
Hardhatter did not even suggest that the police chief was US, nor that he was or was not in reception of any kind of ATC service, nor whether the harbour was his area of jurisdiction and whether he was on duty or not. All it was was a possible scenario they're thinking about in a research institute.
The only reason the ADIZ came up is that they've got a nice way of warning pilots that they're doing something stupid/illegal, and that that same method might be applicable to the scenario mentioned.
If one supposes that the local police chief in his private Cessna 150 is immune, or that holding him equally accountable makes on a "North Korean," then think again.
It's been a while since I've been in the US, but at this side of the pond anything that's not specifically forbidden is still allowed. So as long as there's no published TFR/RA(T)/TRA/SRZ/ADIZ/FRZ or otherwise prohibited area around a warship, regardless of whether it's in port or not, I'm entitled to circle it to go sightseeing as long as I abide by the normal rules of the air. Regardless of whether I'm a private citizen, a police officer on duty or someone else, and regardless of the nationality of the warship. If that makes the commander nervous, he can ask me to leave and if he does so politely, I will.
Let me know if this is any different in the "land of the free" though.