story you've been told. In DNA tests, about 10% of people consistently have a biological father who is not who they think it is; if you apply this percentage back through history, chances are that most of us have some biological ancestors who we don't know about. I've seen quite a few people end up with results like you mention — one guy in my ward was convinced that his ancestry was mostly German, but it turns out that he has very little German and lots of Iberian DNA, which he knew nothing about previously.

Another possibility is that your Danish ancestor(s) somehow immigrated to Denmark from somewhere else, maybe Germany or the British Isles, and their descendents didn't realize that they were biologically/genetically British or German. After all, the Danes invaded Britain during the middle ages, and there was lots of intermixing, as well as many British slaves and wives who ended up back in Denmark.