A few people seem to have skipped over the first sentence of my post. The article said that fertility rate is higher in dictatorships than in democracies at *all income levels*. Meaning if you take any income level and compare dictatorships and democracies in the same level, the dictatorships will tend to have a higher fertility rate.
I've placed a copy of the article at http://www.ibiblio.org/weidai/przeworski.pdf. Unfortunately it does not have a bibliography which makes it hard to determine how the numbers it cites were calculated.