Sounds like a stretch to me. I'd want to hear that they didn't test more than 5 other hypothesis before coming to that conclusion, or the p value was far better than .05. I kind of doubt that either is the case.

This is not a hypothesis testing problem! It doesn't matter what the p-value is, you can't conclude causation from correlation convincingly without showing a mechanism or randomizing or finding a natural experiment. What Pinker's saying (I completely agree with him) is that when the unobserved causal graph between two variables is large enough, there is almost certainly big confounding variables in there you haven't accounted for.

Again -- confounding is not a statistical issue, you can't just get around it by being clever with p-values/Bayes theorem/whatever.

edit: By mechanism I mean a direct mechanism spanning 23 years, not "lead causes brain damage" (because such a high level observation does not rule out confounding sources).