As far as I can tell, this story attempts to make three points:
1. Human genomes tend to cluster into three groups: african, eurasian, and east asian.
2. We expected that the genomes of different ethnic groups would be very different. They aren't.
3. Neutral drift is the major story in how ethic groups' genomes differ.
This pretty much follows the contours of the current orthodoxy in population genetics (with certain distinct exceptions).
So are these three points meaningfully true?
1. Human genomes tend to cluster into three groups: african, eurasian, and east asian.
Generally speaking they /do/ cluster this way. Of course, you can make room for as few or as many clusters as you want-- if it was two, it'd be african/everything else. Three, african/eurasian/east asian. Four, perhaps african/eurasian/east asian/naitive american. Five, perhaps west african/east african/eurasian/east asian/naitive american. From what I've read, the most elegant statistical clusters arise when you allow for four groups (splitting native americans off from east asians). Of course, this clustering gets more complex when you consider admixture populations (e.g., the majority of south america and mexico).
2. We expected that the genomes of different ethnic groups would be very different. They aren't.
It's hard to say this is true or false yet, because we simply don't know how functionally significant these differences are. Two genomes may look very similar, yet be very different in many very significant ways.
3. Neutral drift is the major story in how ethic groups' genomes differ.
This is code for a very contentious question-- are ethnic differences merely skin-deep? The fact is, we don't know yet. There's a lot of research that points to yes; there's a lot of research that points to no. The answer to this is undoubtedly going to turn out to be: yes and no, depending on the context and the threshold you look at.