I was clearly misinformed, thanks for the correction.
The second, that of deciding whether an N (or CH, or RA or anything else for that matter) registered aircraft can be based in another ICAO country presumably comes down to any ICAO member state's discretion. If, say, UK-CAA decide to devolve that to EASA (or HMG gives away a bit more of our sovereignty, and ICAO accepts the renegotiation) then it could yet go to EASA. We shall see !
G