Having done a post-graduate sciences qualification, we were taught absolute proof is a myth, it's all a matter of probability, and subject to revision.
The paper trail may be certain that I'm descended from any given royal, but that's just proof of the paper trail, not of parentage at each generation.
To know that we are not descended from a given royal (in the paper trail) requires tracing all our ancestors back to that generation, which for most of us is impossible.
Given there used to be many more kingdoms and principalities than now exist, and how much smaller the population was, descent from some royal is near certain.