Thomas,
I could prove you wrong...but wouldn't use a source as specific as the Chicago School System, as the data there is rather difficult to find.
I could for instance readily find data concerning statewide funding issue. In my econometrics course, we studied to see if things such as $ spent per pupil and teacher pay in Tennessee had a causal relationship with test scores...and the did not. We also tested for temporal autocorrelation to see if it was a geographic issue, and we were able to get nice p-values allowing us to determine if it was a geographic issue...and it tended to be.
However, at times, I do not always feel that high test scores are linked to greater levels of success, particularly in low income areas. It doesn't matter if you graduated in the top 10% if no one will offer you a job, because there are no jobs. I think something greater is at work here. I think people, in all cultures, are very apprehensive to pick up, move abandon close family ties in search of work. I believe the need for close family connections is far greater in minority communities versus the white community. If minorities are less willing to move to a place where there skills are scarce, then they will always be stuck with low pay due to competition with others with a similar skill set.