While I won't necessarily contradict the eminent authority you quote, I would note that at this time, and for hundreds of years preceding, there was not a country of "Ireland" to be a native of (it was part of the United Kingdom/Great Britain); historically, before 1922 there was only a brief period in the 1000s in which a unified "Ireland" existed (the island usually being broken up into many kingdoms); the settlers of Scots descent did not see themselves as "Irish", in the usually accepted sense of the word "Irish"; and the part of Ireland most of the so-called Scots-Irish came from, Ulster, is not part of "Ireland" today.