We study the impact of secure survey designs ensuring plausible deniability on information transmission in organizations. We are interested in settings in which fear of retaliation makes potential informants reluctant to reveal the truth. Theory predicts that: (i) popular randomized-response designs fail to induce informative reports, because they are strategically equivalent to non-secure direct-elicitation designs, (ii) hard-garbling designs that exogenously distort survey responses improve information transmission, and (iii) unbiased estimates of the impact of survey design on information transmission can be obtained in equilibrium. Laboratory experiments qualify these predictions. While hard-garbling does improve information transmission over direct-elicitation, other predictions fail: randomized response performs much better than expected, and false accusations lead to a small but persistent bias in treatment effect estimates. We show that these deviations from equilibrium can be accounted for in an off-the-shelf model of boundedly rational play, and that this model of play makes specific predictions over the bias of treatment effect estimators. Additional experiments reveal that play converges to equilibrium if players can (socially) learn from cross-sectional data. These results suggest that randomized response cannot be used systematically in organizational settings, whereas hard garbling improves survey quality even under long-run equilibrium conditions.