While the 'State Aircraft' definition of the Chicago Convention applies to all aircraft operated by state, or federal government agencies, this does not imply a requirement to carry state registration. For example, military aircraft will (may) carry a military registration but federal police, customs and other agencies' aircraft will usually carry civilian registration. Also, civil aircraft chartered by the military will obviously carry a civil registration but are considered state aircraft under the Chicago Convention. All state aircraft, regardless of whether that have military or civil registration, will require diplomatic clearance to fly into foreign airspace and will usually be allocated a state callsign as part of the diplomatic clearance process.
The difference between military and civilian registration defines the technical and operational regulation that applies to the aircraft. I can't quote chapter and verse here, but I understand that the conventions applied to the operation of military aircraft is that they operate on a 'due regard' basis. That is, they don't need to be strictly adherent to ICAO or foreign state rules on, say, licensing, navigational equipment, noise and environmental laws or technical equipment carriage.
I have flown military aircraft that were registered on the civil register. They also carried military markings. The technical and operational airworthiness of the aircaft was in accordance with civil regulations and the military aircrew operating them held the appropriate civil licenses and ratings (and were thus liable to civil prosecution if they stuffed up carrying out their miltary duties - but that is altogether another topic).
I would, therefore, agree with ORAC that the reason would probably have had to do with the aircraft or operation not meeting the civil regulations for the particular country or airspace. There would be no need to apply state (military) markings to the aircraft unless it was required in order to comply with the Law of Armed Conflict for a conflict in progress.