Oh but he probably was Scottish:
Scot's Irish.
I have one ancestor, John Kerr, who appears on two or three successive census records as having been born in Scotland. We have since learned that he was born in Ireland. He was - culturally speaking - very Scottish. The Scots Irish never assimilated with the Irish and maintained a different and distinct culture. If the family lore is that he was Scottish, it probably comes from him claiming Scottish descent, the grandkids remembering it and passing it down.
To give an idea of the fierceness of the Scots attitude towards their Scottish heritage, there is a saying that is attributed to John Kerr that was handed down to a grand-daughter who, in her old age, wrote it into the family tree. When he was asked if he was Irish John replied, "Just because a man is born in sh*t, doesn't make him a pig."
He felt so strongly that he wasn't Irish that he would tell the census taker that he was from Scotland.
That statement and the bloody wars that were fought in Ireland (clear up and into the 20th century) show that there was no love lost between the transplanted Scottish "colonists" and the local Irish. Genocides that included the slaughter of entire villages to include little children and babies shows the extent to which the Scottish invaders considered themselves "not Irish." Think of the existing conflict between Israelis and Palestinians and you'll get the idea of some past relations between Scots Irish and Irish. The more recent war in Northern Ireland between the IRA and the UK military is a more recent reminder.
All that said, he may have indeed been born in Ireland but chances are his family was only there for two or three, maybe four generations and came from Scotland before that.
For as long as I can remember he was Scottish. It was handed down from before my Mum was born.
I've seen this again and again in Scot's-Irish genealogies. In once case that I remember a man was writing about his Scottish ancestry and so far as he could tell, his single 4x great-grandfather was the lone Scots-Irish in the family. Yet, six generations later, as a boy, he was being raised to be a proud Scot. He remembers his grandmother instructing him as a child, "And no matter what, always remember that you're Scottish!" He wrote out the math: parents 50% of DNA, grandparents 25%, great-grandparents 12.5%, ggg 6.25%, gggg 3.125% - he speculated that he was three percent Scottish, genetically speaking, and always grew up feeling that he was 100% Scottish. So your family memory of "he was Scottish since before my Mum was born" matches right on target for a Scots Irish ancestor.