The two histograms of pair distances from the two experiments look similar. (Indeed, the two graphs look somewhat linear.) If these two histograms can be distinguished in a statistically significant way from histograms obtained from random partitions of the Rabbis, and if indeed they are significantly proximal then this will also be a very disturbing finding for the integrity of the WRR's paper. It seems that such a finding can be explained much better as a consequence of an optimization process than by some arguments related to the hypothesis of the research. This is a direction worthy of further study. The proximity of the two pair distances distributions looks also quite independent from the similarity in the P2 scores as the later is very sensitive to small perturbations of the partition.
The standard measure for the proximity of two distributions is the supremum norm of their difference, see [4, Ch. 14]. It would be interesting to estimate by a Monte Carlo experiment how significant is the proximity between the pair diatances distributions for the original partition of Rabbis with respect to random partitions.