 Solution

A nonzero contribution occurs when a failure, rather than a censoring, is the earlier observation while both members remain at risk. By the paired log-rank reduction to a sign test, the two possible contributions are $+1/2$ for an earlier A failure and $-1/2$ for an earlier B failure. Under the exchangeable null and the usual independent censoring assumptions they are equally likely, conditional on being informative. HenceOnce the first member leaves the risk set, the second member's later observation adds no group-comparison information within this stratum.