I now had a better look at it, and I think that in particular posts #26 and #31 are important. Anyway I'll give a short summary of how I now see it.
If Jaynes' criticism focuses on Bell's equation no.11 in his "socks" paper, it was perhaps due to a misunderstanding about what Bell meant (his comments were based on an earlier paper).
P(AB|a,b,x) = P(A|a,x) P(B|b,x) (Bel 11)
Here x stands for Bell's lambda, which corresponds to the circumstances that lead to a single pair correlation (in contrast to my earlier X, which causes the overall correlation for many pairs).
According to Jaynes it should be instead, for example:
P(AB|a,b,x) = P(A|B,a,b,x) P(B|a,b,x)
Perhaps Jaynes thought that Bell meant:
P(AB|a,b,X) = P(A|a,X) P(B|b,X)
in which case Jaynes claimed that:
P(AB|a,b,X) = P(A|B,a,b,X) P(B|a,b,X)
This is really tricky.
However, he really was disagreeing with the integral equation.
According to him, it should not be:
P(AB|a,b) = ∫ P(A|a,x) P(B|b,x) p(x) dx
P(AB|a,b) = ∫ P(AB|a,b,x) P(x|a,b) dx
P(AB|a,b) = ∫ P(AB|a,b,x) p(x) dx = ∫ P(A|B,a,b,x) P(B|a,b,x) p(x) dx
Is my summary of the disagreement correct?
What is the significance of little p(x) instead of P(x)?