I am Scottish... as far as background goes I'm around 1/2 Scots and 1/2 Irish. Like most people I'm unsure of my background more than 3 or 4 generations back - and even then there's missing pieces. So could anyone really call themself indigenous Scots unless they can trace more than half their lineage back to the formation of "The Scots" from the Picts, the Gaels and the Brythons. Even then - there has been a lot of migration to Scotland in the last 1000years - especially the lowlands.
I consider myself both Scottish and a Scot... in most contexts I'm sure a lot of people of first or second generation immigrants would too, but why correct them on this issue if they are proud of being integrated into Scottish society? I certainly wouldnt.