The arithmetic gets more complicated when looking at descendants, since the number of each couple's children varies enormously, and the rates of population growth have changed over the centuries. Also, kings tended to have unusually large numbers of illegitimate children. I'd bet that everyone using rootschat is related to each other, having common ancestors no more than 15 generations back - i.e. I have 32,768 chances to match one of my ancestors to one of your 32,768 out of what was a much lower British population than today (the probability being even higher than of matching to one of the 2,500 Scottish nobles I used as an example).
I'm sure the only way you could be pretty sure you weren't descended from ancient European royalty would be if you came from a really remote corner of the world, where Europeans only appeared in the last 100 years or so - isolated parts of Africa or Asia, I'd imagine.
But of course, it's always more difficult to prove the absence of something, and I'd say genealogy was difficult enough as it is!
