From the royals of one country to the "royals" of another...

The Daily Mail ran this piece last week on some of the connections the new royal baby will have with some Hollywood royalty.  As someone who's been trying for over a decade to track down ancestors, I know how difficult it can be... so to see that genealogists have managed to determine that the new little prince or princess will be the Jolie-Pitt kids' 27th cousin boggles my mind.  One of my (possible) branches goes back far enough to allow me to determine my 15th cousins... and that takes us back to the late 1400s.  To get to the common ancestor for 27th cousins... how far back is that?  Another 400 years or so?  Who are these miracle worker genealogists, and can I get them to help me out with my tree?

What am I doing wrong that I've only been able to crack the year 1500 maybe once in over a decade of searching?  (I'm sure having mostly servant-class ancestors doesn't help, but come on...  They say we're all connected if we go far enough back.  I want to see it!)