They then extensively massaged the data to make this difference disappear, which is what yields the headline. They did provide perfectly valid justifications for such, including the fact that IQ testing data was missing disproportionately often from brothers where the brother who had data available was of a low IQ. They thus proposed that the high heritability of IQ would then suggest that the missing data is probably disproportionately weighted against IQ, so that's what they did.
Nonetheless this massaging of the data opens the door to methodological problems. It enables researchers to choose the factors that they consider most relevant and to determine effective weighting for such. You will tend to find in this scenario that individuals who have the preconceived notion of 'x' end up choosing factors that show 'x'. And vice versa for those who assume 'y.' This isn't necessarily even malfeasance, but simply the fact that trying to control for a practically infinite number of possible confounding issues is as much an art as a science, and preconceived notions are going to end up being reflected in what one chooses.
For instance my bias is self evident and if I were going to pursue this sort of balancing I would certainly be sure to try to control for factors such as increasing paternal age, fertility assistance, and other things which can have negative effects on IQ. Some studies have even connected higher IQ parents to various disorders including autism which may mitigate against the missing IQ data bias. Controlling for these things is important. The reason that these researchers neglected them is not out of malfeasance, but because you can come up with a practically infinite number of things you need to control for. And so peoples biases end up reflecting the issues they find important.
The ultimate point is that I think the most impartial idea is to look at the data alone, so much as possible. This study made some fairly extreme changes to the data. Of course if my biases were different, I'd probably be singing a different tune. Isn't social "science" fun?
 - https://www.pnas.org/content/115/26/6674