Yes, pick any two random people on the street of a small town, and they will typically be related at most 7 times removed.
I am a hobby genealogist, and have identified by name roughly 5,000 people in my mother's family tree, alone (I estimate that there are another couple thousand "missing.") There are several fair-sized towns in Redwood County and Brown County, MN - towns I've never visited, incidentally - where I would be third-, fourth-, fifth-, and sixth-cousins with a large percentage of the people I met randomly on the street. (Being a sixth-cousin means that one has a pair of great-great-great-great-great-grandparents in common with the other person.)
My most-interesting observations about my family tree:
1) Lots of people in the U.S. are born, grow up, and die within 100 miles of the same spot. This was especially true of my grandparents', great-grandparents', and great-great-grandparents' generations, but even of my generation, unbelievably many maintain residency in the same corner of the state (apart from their college days, etc.).
2) Americans of Scandinavian descent are remarkably long-lived.
3) After a while, most obituaries become boringly similar (Note to self: Write your own obituary while you still have the time!).
4) Establishing a "dynasty" requires - besides herculean efforts - that the members of that nascent dynasty be aware of and have agreement on what they have set out to do, but it is possible to achieve and maintain "super-wealthy" status by dint of one's collective efforts - by essentially forming a "family syndicate." The main barriers are a) divorce, and b) the resultant dispersal of wealth to non-family members (step-relatives). (However, the one instance of success I've identified in my own extended clan was founded in the gray beginning on what would be considered today to be a grossly unethical act.)
Regards,
I, too, am a Bush cousin. But think about it: anybody whose ancestors were early American settlers, as the Bush family ancestors were, is likely to be related to other descendants of early American colonists. There were so few people — and they had such large families — that it’s not in the least bit surprising. So the Bushes and I share one set of many greats grandparents, big deal.