I'll have a stab at an answer Ruskie, but I don't understand it all in any detail either.
However, segments of DNA inherited through family relationships become watered down (for want of a better term) over generations, and can either disappear completely or become so small as to just become random noise after several generations due to both the randomness of inheritance and the addition of segments inherited from subsequent descendants of more distant ancestors in your line and their spouses or partners etc.
The ethnicity reference panels chosen by Ancestry and other companies are supposedly identified in part by evidence or belief that their families have been present in a particular region for many generations. When each Ancestry test is examined for ethnicity, rather than looking for segments inherited by family relationships, the full sample is split into segments that are each examined for evidence of what are considered to be regional inheritance patterns - believed to be common to general populations rather than only passed down through specific family lines by relationship inheritance. When I say that they are not looking for segments inherited by family relationships, that's not strictly true, as Ancestry at least use a process which attempts to identify those segments and actually strip them out of the ethnicity calculation.
It's a lot more complicated than that, but they aim to identify regional similarities in the split segments that have been passed down through populations living in those locations and which remain pretty much unchanged over a longer period of time than the reach of family inheritance alone.
The results are probabilities, not guaranteed facts. When they assign a particular string found in your or my DNA to a region, they believe it matches that region to the highest probability of what may be several or even numerous indicative matches to different regions entirely. They aim to achieve an overall accuracy of more than about 80%, but for some regions the accuracy may be only 50% or lower.
There is an interesting and even better explanation of Scottish ethnicity by way of an example in Ancestry's white paper:
"For example, in Figure 4.4 there is assignment to the Scotland region in the Brittany area of France. This makes sense because of shared Celtic ancestry in both Scotland and Brittany, where the Celtic language Breton is traditionally spoken. Scotland estimates in England also likely reflect the history of Celtic ancestry in that area."
In other words, an ethnicity allocation to Scotland may not have any connection to the country of Scotland at all, but could relate to the fact that your ancestors came from Brittany in France and settled in England. I have an allocation of 8% Scottish ancestry in my ethnicity estimate, which derives from a probability of 0% to 25%. In other words, Ancestry are saying that it's possible despite the 8% allocation that I might have no Scottish ethnicity at all. Certainly, I have no known line of direct descent to Scotland, but I do know that both my mother's and father's surnames are believed to derive from names that originated around the Brittany/Normandy border region.
But does that account for my Scottish ethnicity allocation, or is that purely expectation bias on my part, in trying to justify an allocation that may not in fact even exist?