The grey area appears to be flying an N reg outside the USA on an airmans certificate linked to a UK licence.
I recall busting the airspace around the Woomera rocket range in Australia flying an N reg Lance from Ayers Rock across the outback in 1989. On landing at Port Augusta I was asked to phone Adelaide who berated me,asked for my Aussie licence details (I had none at the time), and let me go because they had no jurisdiction. They were a bit shocked when asked for my point of departure and I replied Detroit.
However Australia did not allow N reg aircraft to be operated by residents for longer than a year.I had to change the the aircraft and my licences to comply.
That is to avoid US registration disguising aircraft owners behind shell companies using it as a flag of convenience.
Most of the current fleet of N reg UK based aircraft are rarely owned by US citizens.
The FAA certificate is clearly linked to the UK licence so surely the buck stops with the CAA?