I find that to be a weak argument. The "main relationship" does not "stem" simply from a shared head of state. Nor does anybody claim that Gibraltar is "part of the UK", but rather that their status as a BOT means that they are subject to UK sovereignty and jurisdiction. It's quite true that Gibraltar is mostly self-governing, except in matters of defence and foreign affairs, which are managed centrally from London. However, that doesn't mean that ultimately they are not subject to UK jurisdiction. It's quite reasonable not to care, but it's still good to know.