Am I Reading This Wrong?

Krugman reproduces the above graph and writes:

[T]his recent survey paper (pdf) on teen births, which are much higher in America than in other advanced countries. The authors find evidence suggesting that inequality and lack of mobility are central, another sign that Wilkinson-type views about the corrosive effects of inequality are going seriously mainstream. ... [I]nteresting stuff — and more evidence that we are gradually poisoning our society with inequity. 

I've only skimmed the paper -- which was published in the Journal of Economic Perspectives -- but I don't read it the same way at all, nor do I see it from that graph. What I see is that the discrepancy is mostly driven by whether the mother is well-educated or not. As far as I know whether or not students graduate from high school is not a function of inequality, but of poverty and other socioeconomic and cultural factors. Indeed, that is what the authors of the report conclude:

We believe that the high rate of teen childbearing in the United States matters because it is a marker of a social problem, rather than the underlying social problem itself. If a teenager has a baby because her life chances seem so limited that her life will not be any better if she delays childbearing, then teen childbearing is unlikely to be causing much of a detrimental effect. Our review of the evidence is consistent with this position.

At times the authors seem to think that poverty, social mobility, and income inequality are the same thing. I would be more likely to attribute all of them to common underlying causes that has been transforming the global political economy over the past 20+ years. In any case, the authors argue that improving economic opportunities is the way to improve this statistic. In fact, they explicitly rule out increased income inequality as playing a causal role in recent trends, noting that teen childbearing has been going down over the past generation (implying a negative correlation with income inequality if there's any relationship at all):

One thing that we have not done is explain the dramatic decline in teen childbearing in the United States over the past 20 years. Although we believe that inequality and lack of opportunity explains a substantial share of the geographic variation in teen childbearing, it is not a candidate explanation for the downward trend in the United States over the past two decades, primarily because the 50/10 ratio that we rely on as a measure of inequality has not changed much during this period (although our results are insensitive to the specific measure used).

So what on earth did Krugman read? If teen childbearing has been going down at the same time that inequality has been going up that would seem like prima facie evidence that income inequality is not causing teen childbearing.