This is so widely known, even without the study, that it doesn't really need to be pointed out. This falls in the category of stating the obvious.
Friedman states this, which is one of the most useless statements I have ever heard:
To be sure, there is no substitute for a good teacher. There is nothing more valuable than great classroom instruction. But let’s stop putting the whole burden on teachers. We also need better parents. Better parents can make every teacher more effective.
The problem with these types of columns is that how good a parent is isn't really subject to change. People have known this for so long that it's implausible that any amount of moral exhortation will get more parents reading to their children, this is a cultural habit that would have been known in a rough form in ancient Rome or China. We don't really know of any reliable way to make better parents, though redistributive policies like income supports, child care subsidies, and better transportation policies do help indirectly. This kind of statement is like saying the solution to our health care problems is for people to become healthier. No shit. Where's the magic wand that will achieve this? We could also stop war if people were less violent, church attendance would go up if people were more godly, and our political system would be less of a mess if people were more trustworthy and less selfish. But they aren't.
The world has problems because people aren't perfect. The question is how do we deal with imperfect people who aren't perfect. Wishing people were better is worse than useless, it is actively harmful because it attempts to shift the locus of change from things we actually have some control over, like the incentives to attract good teachers and policies like the length of the school day, to things we have absolutely no power over, like how good parents are. How good of parents the people having kids are isn't really a manipulable variable, unless you're an advocate of draconian social darwinism (or willing to embark on widespread redistribution that wouldn't otherwise be embarked on as a result of it spurring better parenting, which seems implausible). The purpose of this research is to help understand which kids are going to have difficulties so that we can focus research on those kids which have the biggest deficits.
Indirectly, it does also emphasize the importance of non-educational factors leading to social breakdown on education and thus upward mobility. But we know with certainty that simply pointing out individual's failings does little to spur better behavior. Its best we focus on what we can control with social action and policy rather than getting distracted by factors that, while powerful, are completely outside our realm of control. Of course, this kind of dialogue does seek to shift things towards individual responsibility, but this does little but reinforce existing inequality of opportunity because we know with some certainty that people have always been about the same. Knowing that many people aren't good parents, and doing nothing about it because things would be better if more people were good parents, is simply an abdication of our individual responsibility to seek to grapple with or world as it is, rather than as we wish it would be. Everything would be great if everyone was good at everything they did and thus raised children that would be great at everything they did too, but this isn't Lake Wobegone, so we need to focus on things like better teachers and schools that can make up the deficits for bad parents. Change the things we can, rather than wish our troubles away by pushing responsibility for them off on someone else.