[brigandish]

> But Europeans are diverse mutts as well.

Speak for yourself, because

> If their great-great-grandfather was Scottish, they then assume everyone before him was 100% super duper Scottish

That is, indeed, the correct assumption to make. I would recommend having a look at the work done on population genetics at Oxford University’s People of the British Isles project[1]. Even their homepage should relieve you of some misconceptions:

> The People of the British Isles (PoBI) project was initiated by Sir Walter Bodmer in 2004, in an effort to create the first ever detailed genetic map of a country. The United Kingdom’s history bristles with immigrations, wars and invasions, so the PoBI researchers faced a tremendous task in investigating how past events impacted the genetic makeup of modern British people.

> Results included a map (image below) showing a remarkable concordance between genetic and geographical clustering of our samples across the United Kingdom.

[1] https://www.peopleofthebritishisles.org/