I didn't say you claimed it was proof. I said "evidence" and I think that as a matter of evidence it is pretty weak.
Regardless, in practice people do treat it as proof. Before I move on to the other arguments supporting oppression as an explanation I want to drive home that point: there is hardly ever a serious attempt to rule out other possible explanations for disparities, and to suggest that anything other than racism/oppression might explain those differences opens one up to accusations of racism.
Merely referencing Jim Crow is not enough. It ignores both all the ways in which Jim Crow was ineffective at its aims at the time, as well as the seismic cultural and legal changes that have occurred within the intervening years.
It also fails to account for the success of various other minorities (Jews, Nigerians, descendants of Caribbean slaves, various Asian groups) - many of whom also have faced very serious oppression (including outright attempts at elimination) in the very recent past.
None of this is to say that racism does not occur, but I have yet to see a (non-circular) causal explanation for how that can account for a significant amount of present disparities.