Sorry for the late response. I haven't gone to the links yet but the quotes in italics give me pause. They seem to be at pains to state things in a way which looks like it means one thing but may mean another. The second sentence is a nice start to an investigation but is not evidence really, just a temporal association. The third sentence is about poverty, not integration.

The fact that the gap is larger in segregated districts is difficult to interpret without knowing if the comparison is to the population as a whole (i.e. blacks in the district to whites as a whole) or within the district (i.e. blacks in the district to whites in the district). I'd also want to know if how those districts compared to other districts. Were these high achieving schools? Low achieving? Somewhere in the middle?