Most of us posting probably are. I read somewhere that if you are of European descent on both sides, you just about a 100% chance of being descended from Charlemagne.
That means there is also a good chance we are related to people like Louis the Sluggard and Charles the Fat. That's kind of cool. I'd like to mix in some Ethelred the Unready and Hardicanute.
The problem with the Every European is Descended From Charlemagne quote is that its reasoning is derived from numbers of hypothetical ancestors giving undeserved weight to assumed randomness without giving due credit to inbreeding.
Royal inbreeding is well known. I can't remember which exact Hapsburg it was, but I recall reading that while, theorectically, one can have 64 different great-great-great-great-grandparents, this particular Hapsburg only had 16 or so.
In small villages, where most of the European population lived, poor transportation and local geography would result in a great degree of local inbreeding with the same families marrying each other for centuries.