It was the family factors that carried the day in determining the children's performance in high school. It wasn't the school that they went to:
The idea basically being, that it's what's happening in kids' families and the kinds of conditions that they're able to purchase for their kids and the circumstances that they're able to provide for their kids over the long haul that really matter in.
When the study looked at the low-income kids in the sample who were in private schools, it didn't see any advantage to private education there either.