I have no idea if the Scots think or joke that the English are stupid, but can say that the English have a joke pattern of "An Englishman, an Irishman, and a Scotsman…" and it's always and only the Irish who are picked on.
It is/was the same pattern in Norway and Sweden, and to some extent Denmark, with those three. I suspect a whole lot of these were recycled by publishers of cheap joke books and magazines.
The Basque person in the joke is always called Patxi, a stereotypical Basque name (kind of like calling an Irish person "Paddy").