Proving that children who are raised by their biological, married parents* do better than other kids requires more than just looking at statistical attributes of those kids and comparing them to other kids. But the "marriage will solve everything" crowd relies only on those sorts of statistical measures because more accurate methodologies refute their claims.
It's just bad social science. The assumptions you have to make to draw those conclusions are large and counter intuitive. For example, if you wanted to say that kids who are raised by their biological, married parents are more likely to go to college, then you'd have to assume that neither having married parents nor getting a college degree are correlated with other forms of privilege (race and parents' income and parents' education and national origin, etc), which is a joke.
Moreover, even if they crunched the numbers in a way that controlled for other, measurable factors like parents' income, they'd still have to assume that they accounted for everything that cannot be measured as well (parents' happiness, community support, social skills, etc), or at least assume that those unobservables don't matter. Which is also a joke of an assumption.
The more I learn about human behavior, the less natural the platonic ideal of the nuclear family (one mother, one father, their biological offspring in one house, to the exclusion of extended family and friends, with no significant ties to other people who aren't related by blood or marriage) appears to me. Kids should not just have friends their age; families need community support; each parent should have their own lives and social networks; and the bias should be towards openness, not exclusion, in home and community.
I don't know if the statistics back up my instincts, but at least I know I'm not just making some up to pretend like I have science on my side.
*I left the word "heterosexual" out for a reason: the National Review's article doesn't directly argue that only straight parents are good, even though it's probably what the authors believe. Also, I've heard plenty of gay activists over the years make that same argument (i.e., Marriage, the piece of paper itself, will make kids of same-sex couples succeed).