The Scots (originally Irish, but by now Scotch) were at this time inhabiting Ireland, having driven the Irish (Picts) out of Scotland; while the Picts (originally Scots) were now Irish (living in brackets) and vice versa. It is essential to keep these distinctions clearly in mind (and verce visa).
I hope you have got that clear, because at the time of independence it might become important!
The book is a masterpiece of historical mis-information, written by W C Sellar (Aegrot: Oxon.)** and R J Yeatman (Failed MA, etc., Oxon.). They take the bits of history that you think you remember and they weave a delightful tale around these factoids, misleading the unwary and yet in a strange way teaching the curious.
Knowing the book quite well, from so many readings and re-readings that my treasured copy of the book is falling to pieces, I sometimes come across a bit of history and think "Aha!! That's what they meant in 1066!" Knowing that usually makes the book even funnier.
** Small note: Aegrot is short for 'aegrotat', the Latin term to describe a degree awarded even though the student was too sick to complete the course. So one author never took his exams and the other failed. Both have become famous in spite of their Oxford educations. Of course both might be joking.