And how does one not imply the other, or are you suggesting that one parent born in County Cork of its native stock, and the other born in Hokkaido are going to have just as likely a chance at the same genetic distance as both parents born in the same geographic region?

People in nearby villages in sub-saharan Africa are likely more diverse than people on different continents outside. People outside Africa are remarkably inbred (the bottleneck is measured in a few thousands at most).

We’re reliably informed that race has no biological basis and differences are greater within groups than between them, so isn’t the answer obviously yes?

Race is a self-described proxy variable that correlated with genotype. I know some folks (even very well-educated and highly placed) deny that.

Still it's better to use the term "genetic history" because it's a much better variable to describe distances between people.

That's true if you include Africa, but it's not nearly as true if you exclude it. But "race" of course doesn't cause this, as it can't cause anything.

(And people living in Japan aren't genetically homogenous of course.)

I imagine those would be highly correlated too.