Every time I see a study like this, I reverse the premise and see if it makes sense. In this case, I would ask this. Instead of poverty cause low brain development, does low brain development cause poverty. I would argue that much of IQ is inherited, either through nature or nurture. To put it bluntly, stupid parents tend to have stupid kids. Its also clear that a lower IQ very much limits your earning potential - thus puts your family in poverty.
So, I think this study is balogne. All it says is poor people tend to be on the lower end of the IQ scale, and so are their kids.