Northwind – substitute The Economist, a publication with a global audience, and you see multiple references to the border, north of the border, sound of the border etc.
North of the border, south of the border- you seem to be missing the point, nobody objects to that at all Our side, the other side, is what annoys people, because it is assuming that your readers are on your side. It’s not specifically the choice of words, it’s the us/them.
English, Scottish, UK, global publications can use the term in a way that is completely inoffensive – as it should be. As has been noted several time, the context of the OPs quote is unclear (I think) but the sensitivity is (IMHO) verging on the absurd.
The exact context of the quote isn’t important, because it’s just one example of a common thing. The OP isn’t raising it because one person did it. Quite a few people have pointed that out tbh, and expanded it to other fields where the exact same thing happens- “national” news spends extensive time on English issues, for example. MPs worry about the west lothian question because they just assume it’s right for scottish matters to be discussed in scotland but english matters to be discussed in the UK parliament. And so on.
And fwiw, I don’t see any outrage, just mild irritation.