I think that's pretty accurate, but of course it does depend on what the Sutherlander meant by Southerner. It's all relative. Perhaps they would call me (close to Stirling) a Sassenach, but I would only use it for someone from England, and possibly even excluding people from the North of England who speak a dialect closer to Scots than to Standard Southern English, which is what their dialect is more closely related to historically.
To make the point about it being relative, Sutherland itself means 'Southern land', just from the point of view of those even further north. It is Norse in origin, and reminds us that they were not Saxons in Sutherland, meaning that the Saxons were indeed southerners from the point of view of the Sutherlanders.
Actually I come from the southern part, the land of the South Saxons, which is usually abbreviated to Sussex. Other people come from the land of the East Saxons (Essex), the West Saxons (Wessex) or somewhere in the middle (Middlesex).
Precisely. You have given the Gaelic spelling. The more common English spelling is sassenach + variants. Originally the word would have covered lowland Scots as well but now it just refers to the English. It is derived from Saxon, so really I am just a Saxon and I come from Saxonland.