Two points:
1. when there are relatively small numbers of X, I agree that we should not expect the set of all X to proportionally represent the whole population. This leads to the question of what a "relatively small number" is, and while there is a mathematical/statistical way to answer this (sampling/set theory etc.), I think there's room for there to be a political/social dimension to it as well.
2. it is true that the Nobel situation does not indicate a Jewish cabal. However, it is interesting enough to raise questions about the specific histories of those winners, and whether there was anything about their being Jewish that helps to explain their success (I have no idea of the answer). Likewise, I think it is absolutely worth wondering where all the white rappers are, even though their absence doesn't indicate discrimination or a cabal.
I largely agree with your final paragraph.
Is your point that board members should be randomly drawn from the population like jury members?
Why do you believe that all positions in all domains should be perfectly proportional with the underlying population across the six dimensions you've decided to care about? Is that reasonable?
That is not to say that discrimination is imaginary. It is not to say we should ignore it. It is to say that disproportionate outcomes are not evidence of discrimination. In other words, the fact that 20% of Nobel prize winners are Jews is not evidence of a global Jewish cabal. Nor should you stay up at night wondering where all the white rappers are.
If you actually want to help disadvantaged groups, focus on existing programs that don't effectively serve those groups. Like public schools. How can we make public schools work better?
The truly inane thing about mandating one black/gay/woman/whatever on every board is that those people won't be disadvantaged. They aren't going to invite people off the street to sit on their boards. It's just cosmetic bullshit.