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 we're talking about physical movement and mathematical probabilities, then we're discussing whether or not the various populations (such as those in New Guinea) were hermetically sealed or was there any movement at all in the last three and a half millinea.
The world population back then was less than 100 million. For you or I to not be descended from cousins there would have had to have been a population of 4,789,048,565,205,902,682,369,834,459,844,000,000, 000,000,000,000,000,000,000. So we both agree that
1. We don't know anything for sure
2. People intermarried a lot
3. People moved around a lot.
We could go at this strictly from Sacred Texts also but (please forgive) I'm not sure where you're coming from.
Depends on how you define "recent".
Well said.
WEll, that is an extreme example -- however, most of the peoples populating the Eurasian continent and Africa north of the Sahara have had regular contacts for millenia. The more apparent are the Caucasians -- you can most definitely say that if you have any amount of Caucasian blood, you are related to those who faced CAesar's troops in 54 B.C. and those who created the VEdas in the second millenia and those who built the pyramids and those who trudged with Moses.
There are extremes such as the MElanesian tribes in Papua New Guinea (Australoids I think and related to the Australian Aborigines) or a remote South American tribe or the Bushmen. Most other groups are not that isolated