Nice interview! I actually made a documentary a few years ago on the topic of school choice within one of the top-rated school systems in the country (Howard County, MD). The link isn't up anymore, but I will try to dig up a copy and post it myself sometime. What we (or, more accurately, the mom who did most of the research for the doc) found was even more insidious than what Jason describes here.
Essentially, this school system had "good" neighborhoods, and "bad" neighborhoods, and corresponding schools for each. There had been some ability for parents to move their kids around between schools within the system, but they started really restricting that when a bunch of parents got together and paid for a bus to take all of their kids to the school they wanted to go to.
Here's the insidious part: When we looked at the history of approvals/denials of requests to transfer from one school to another, there was a clear pattern of discrimination against requests coming from the "bad" neighborhoods. Their requests were denied at a much higher rate than were requests from the "good" neighborhoods. (And of course, requests coming from school administrators were ALWAYS approved!)
The thinking of some of the policy analysts we spoke with was that this problem was exacerbated by NCLB - because of the increased emphasis (and financial incentives for) on test scores, school systems became even MORE reluctant to bring lower-performing kids in to a school that had very high scores. Never mind that doing so would probably have helped the child from the lower-performing school, and would not have harmed the children in the higher-performing school. It's not about the children.
For me, the whole thing was a very powerful lesson in how the government schools utterly fail those at the very bottom.