Last I was in Denmark, I heard yet again, how some of us are descended from the Count of Hardenberg. There is, true enough, a connection, but it's a little further away than the myth would have it. What I heard was that Karoline, the oldest daughter of Lars and Ane Kirstine, was actually the daughter of the Count, that Margrethe was also of noble descent, and that her baptismal certificate shows this. Pure myth!!
The real story is that Karoline, Ane Kirstine's oldest sister, is probably the offspring of the Count of Hardenberg. Dorthea Larsdatter - the mother of Ane Kirstine - was in service on the estate, and very conveniently became pregnant at the same time as the Countess. Conveniently, because at least in those days, countesses did not breastfeed their own children, so Dorthea was available to provide this service at just the right time, probably because the Count had made sure she would be. This is only speculation, but speculation based on logic. Firstly, this sort of thing was common practice, and secondly, Dorthea was given a small farm belonging to the estate. Back then, it was highly unusual for women among the 'common folk' to own real estate, so we might conclude that she would have had to provide quite the special service to deserve this kind of payment. Whether Lars Olsen was chosen for her or he was her own choice, I don't know, but in any event they were married in order to make everything look decent, and lived on Dorthea's farm, which Lars tended, while Dorthea served first as wetnurse and later as nanny at the manor.
The story continues with Dorthea's second child also having been fathered by the Count, and arriving at the same time as the Countess' next one. I don't know if that is true, but this continuation is no doubt the reason for Margrethe's inclusion in the myth. The thing is though, that Margrethe wasn't Lars and Ane Kirstine's second child, Morten, who died from diphteria in 1890, was, and besides, they were both born one generation after the Count's involvement.
The myth undoubtedly originated because both the oldest sister and oldest daughter of Ane Kirstine bore the same name: Karoline. I can't imagine it would have been because we want to be nobler than we really are. I think we're quite noble enough.