Looked at from angle number 1, these two distributions don't look much different:
Looked at from angle number 2, they look even less different:
At this point Lewontin and his ilk throw up their hands and say "race is imaginary." (Technically they say race is a social construct, but most people don't know the difference, and they know that.)
They never bother looking down another axis, which the man on the street does uncannily well all the time without any help from mathematics and despite the fevered desires of the capital-P professors:
The two populations are almost completely distinct.
In mathematical terms, the vector perpendicular to the viewing angle of the last picture is called a discriminant. Now, it is true that when no or only a poor discriminant can be found, there certainly is more variation within groups than between groups. But the reverse does not follow.