Not quite true. If you wished to be addressed by the title of 'Sir' or 'Dame,' you would have to be a British citizen, but a non citizen can add letters after their name, e.g. Bob Geldof, KBE, remains a citizen of the Republic of Ireland.
I believe Commonwealth citizens (at least, those from countries that share a monarch with the UK) are entitled to use 'Sir' or 'Dame' as well: though Canada, for one, seems to take a dim view of its citizens accepting British honours.
