I guess I don't get it. It's possible to select by race (or at random) to make the demographics of a selective high school equal to that of the whole district. But then you get lower performance, as they've shown.

What doesn't seem possible is to select by race to match the district and get the higher performance of merit-based admissions, when there are confounding race-based factors like having kids and only 1 parent or less education. The only way it would be equal is if all races had the same level of education and probability of single parents (or if these two things are not contributing factors to a kid's school performance).