I don't think those in the North of England who use it this way do so because they are less well-off, but more likely because they are less educated. Or do they teach this usage in the schools up there?
Well, I don't know that it's about being less educated per se. In all likelihood, and as far as I understand it, "be sat" is grammatical in their dialect, and so they learn it the same way other speakers of English would learn "be sitting": from acquiring the language as infants. In the same way that in a certain African American vernacular, double negatives are grammatical.
As a native speaker of Dutch, I cannot speak to the correctness of my personal grammaticality judgments about English (though I started learning it almost soon enough that you could call me a native speaker, I wasn't quite young enough). However, I can speak as a former linguistics student. Granted, linguistics is about description, not prescription, so if you wanted to
prescribe what is grammatically correct rather than
describe native speakers's judgments, you could do that (as I liked to do prior to learning about linguistics). In that case, you're probably correct in saying that "be sitting" would be the more commonly accepted syntax.
I don't agree with the notion that "be sat" in this context would mean that someone else sat the person down there (the causative use of the verb). That would be the necessary interpretation in the common dialect of English, where "is sitting" would be used as the default. However, that does not seem to be the intended meaning of speakers of the dialect whose speakers use "is sat" in this manner.