Stray Fin, that's weird, but it adds another piece to the jigsaw.
As with your good self, I have a UK Passport thanks to Senior (also ex RAF) and a NZ one by birth.
However, my British passport bears the stamp "British Citizen" because, perhaps out of foresight, Senior thought to register my birth (and those of my sisters) with the British High Commission here as "British Citizens born to a British Citizen abroad".
Apparently if this is not done, your passport will say that you are a "British National" - which is not the same as being a "Citizen", and although your passport allows you entry, it does not of itself guarantee you the right to residency in the UK.
Hair-splitting bureaucratic BS, but perhaps it sheds some light on your situation.
AP, good to hear you are doing well, keep it up, and come home when we have some F-15s and F-16s for you to instruct on