Airspace has nothing to do with it - only which licence the country accepts for flying its aircraft, and these rules vary country by country.
I would take issue with that. Airspace has everything to do with it. The country in whose airspace you are flying has sovereignty over that airspace and can make whatever rules it pleases subject to its international obligations. Those international obligations (under the Chicago Convention) mean that it must grant foreign registered aircraft the right to perform international air navigation based on flight crew licences issued or rendered valid by the state of registry. If it chooses to make more permissive regulations than the state of registry does, it's difficult to see what jurisdiction the state of registry would have, particularly if the crew were not nationals of the state of registry.