This, as you say, is a very old chestnut.
I dont think you are quite correct - I think the key words are both country and issued.
I also think that ultimately it doesnt really matter what teh CAAs or FAA interpretation is - unless of course that suites your case.
On the one hand they are not going to set aside their interpretation, but if you dont like it, their interpretation renders itself liable to being test in the Courts.
In reality the whole point is academic because it is highly unlikely anyone would have the energy of resources to test anything like this in the Courts.
For the fun of the argument the Americans of course dont understand any other way of doing things than their own. They consider their own country to be a series of States that form the whole. Some of us may consider the United Kingdom to consist of a series of countries, principalites, provinces and dependencies that form the whole. Others may be more comfortable with this term referring to the British Isles. The United Emirates doubtless have their own view as to whether they are one country or something else.
Personally if the CAA told me I could fly to the CI in a N reg and I had that in writing that would do for me, but, God forbid any accidents I would probably copy the letter to my insurers and get them to confirm they were happy with the CAAs opinion.