What I mean is, the real history consists of the stories that are remembered long after. How far they correspond to the facts is a secondary matter - the stories are the things that tend to shape how people behave.

Pretty obviously in saying "your streets" Larry was referring to the streets in the kind of place where Gareth, with whom he was arguing, lives. The IRA did all kinds of unpleasant things, but they were never an army of occupation in a foreign country, which was what was being discussed.