The coupler Eve did not monitor: a black-box cavity cheat

Eve receives two average photon counts, while a monitor watching for external leakage may register nothing. Can she conclude that Alice and Bob's opaque cavity devices did not communicate? We give a constructive counterexample: two independently operated controls activate a shared beam-splitter interaction after the inputs arrive. The parties report genuine sample averages, and a fixed local threshold converts these reports into a CHSH game with expected score S=13/4 for four repetitions per block, approaching 4 for large blocks in the ideal model. This exceeds the usual 2 sqrt2 quantum benchmark because the devices interact during their response. A separate dispersive-bus model explains how substantial exchange can coexist with a small probability of a click in a specified leakage monitor; an illustrative open-system calculation exhibits both effects without postselection. The output marginals nevertheless reveal signalling. The example separates three questions: whether the reports are honest, whether a monitored port is quiet, and whether the devices are physically isolated.