Maybe it's unfair to call that "torturing the data." Such regression analysis is a valid statistical tool. But it's prone to researcher bias. Statistical hocus-pocus is not the best way to compare schools. "Ideally, to ascertain the difference between the two types of schools, an experiment would be conducted in which students are assigned (by an appropriate random mechanism) to either public or private schools." That quote, believe it or not, is from the study. But the ever-scrupulous journalists at The Times didn't find that "fit to print."
In any case, it's telling that they put so much emphasis on 4th and 8th grade tests. That's just the beginning of a student's education. American 4th graders do pretty well in international competitions. It's by 12th grade that Americans are so far behind. The longer they spend in America's bureaucratic schools, the worse they do. I'd like to see The Times publish results of 12th grade comparisons, but I won't hold my breath.
Why are the mainstream media so eager to defend a unionized government monopoly? Maybe The Times gave the "adjusted" test data (and an earlier version of it published in January) so much play partly because of the editors' dislike of "conservative Christian" schools (which did poorly in the study) and the Bush administration (which has talked about bringing market competition to education).
But I suspect the biggest reason is that the editors just don't like capitalism and free markets.