"The past thousand years" sounds odd to me. Obviously we are all related if you go far enough back, and studies of this sort are merely parsing minor differences within the same tribe. That said, I would have guessed that to find "all Europeans as one big family," one would have needed to go back perhaps 2,500 to 3,000 years, if not to the end of the last ice age. The rise of agricultural and, later, urban cultures tends to fix people in place.
Exactly. I remember reading Gibbon (Rise and Fall of the Roman Empire).
He talked about the very common practice, in ancient times, of lifting whole subject populations out of their home area and transporting them hundreds and thousands of miles to be sold into slavery.
Of course there was the subsequent mix of DNA from that point on. I always wonder if the geneticists who track this kind of thing, take into consideration that many groups got ‘transplanted’ in this way.