As a civil engineer I can guarantee that every time you walk into a building you're staking your life on both.
The math isn't too hard to follow. We all had two parents, four grand parents, eight-- well, you get the picture. Pat Paulsen said this proves the world population is obviously shrinking, but I think it shows that the world's common ancestry could be as recent as about 30 generations, or 600 years.
Hopkin took this idea a step further and plugged in how much people travel and showed that our common grandpa shouldn't be farther back than 3500 years.
It's "probably" true.
It's probably not true, since there are scads of assumptions in any such a simulation, most of which are probably either untested or untestable. Is it really reasonable to expect that every member of an isolated tribe in the mountains of New Guinea, that had never even seen Europeans (much less intermarried with them) before 1950, shares a recent common ancestor with a family in Iceland that has a complete geneology going back to 800 AD? Not hardly.
If you ignore the evidence, and follow your imagination, anything is possible.
Aborigines in Australia, Pigmies deep in the jungles of Africa, Indians in the Americas, Blonds in Europe, and black haired Asians of which all have traits peculiar to their ethnicity and uncommon to all need a vast amount of time to acquire these isolated differences. It did not happen a few thousand years ago.