While I would recommend following the "family lore", I'd still take whatever measures you can to verify. The "Scots Irish" tag had been tossed around my family for quite some time but the discovery of some folios from a great-great-great-uncle's journal showed that, while his grandfather was born in Ireland, the family certainly wasn't "Scots Irish". My sixth great grandfather went to Cork Co. along with the military in 1798 (though we're unsure in what capacity - he was certainly not an officer but was able to take his young wife with him). After staying some years in Cork, the family found their way to Edinburgh.

So look into it, but when all else fails the best you can do is trust what you've been told.