I've never read any linguistics book that says anything other than what I wrote above. They all explicitly mention that High German is called such because it came from the higher terrain of Germany.
There's no relevant to what you've said about there being different varieties of low German. That was never in dispute and is not, in fact, in dispute. I even mentioned it in my post.
Don't let the current distribution of dialects fool you. Historically, places like Muenster would have been solidly low German. Once East Central German became the prestige dialect, it spread and supplanted the other dialects, even in the north. The same thing happened in France, where historically, what we now call French was in fact a minority language from the areas around Paris.