Earlier quoted context omitted.
Post hoc ergo propter hoc is one of the classic logical fallacies[1]. You persist in the assumption that poverty causes lower IQ, rather than the possibility that both poverty and lower IQ are correlated because they share a common cause. [1] See http://www.skepdic.com/posthoc.html
The way you do a controlled experiment in science is that you have a number of subjects, you subject only some of them to some new condition, and then you look for statistically significant differences between the group subject to the condition and the one that wasn't. That was what happened in the study I mentioned. Now, you can say that this wasn't absolute proof and you'd be right, because science doesn't provide…
Nutrition is a really low hanging fruit, and you have to be pretty poor for it to have any effect.