
Take away the public/private school question for a moment
Similar results (although not quite as extreme) can happen between public schools at different levels of spending, too. The local large school district has, I think, the second highest spending per capita than any other school system in the state - yet produces pathetic graduation rates and test scores.
Clearly there are other factors involved.
And it isn't even an inner city/suburban question - yes, Marva Collins founded a private school, but in working with public schools in some of the seediest areas of Chicago has led those schools to significant improvements in math and reading skills. She's able to take some of the supposedly least teachable kids and teach them.
French Zombies are zapping me with lasers!