Large language models are increasingly deployed as advisors whose objective is not aligned with the user's: recommenders optimize for engagement, sales assistants for purchases. Whether they stay truthful when honesty conflicts with their own payoff is a core alignment question. We turn the canonical Crawford-Sobel cheap-talk model into a pre-specified benchmark for LLM honesty under preference misalignment, in which theory supplies an exact oracle. A sender observes a state omega in [0,1], wants the receiver's action near omega+b, and sends one costless message to a receiver whose ideal action is omega. For the positive-bias grid b in {0.01,0.04,0.08,0.12} the exact most-informative partition sizes are 7,4,3,2, with oracle normalized mutual information 0.5294, 0.3268, 0.2205, 0.1829. Extending a pre-registered 4-model run of 12,000 sender calls to eight models across two capability tiers and 39,569 logged calls, all models over-reveal relative to the most-informative equilibrium by 1.8 to 4.5x: pooled normalized mutual information stays at 0.82-0.96 where the oracle prescribes 0.18-0.53. Informativeness declines with bias as predicted (beta = -1.71, t = -7.50) but never approaches the strategic optimum; rather than coarse partitions, models show near-full revelation with a constant upward offset tracking their bias (linear exaggeration). A structural hint separates capability from propensity: told the equilibrium partition size, reasoning models state a correct Crawford-Sobel cell in 0.20-0.99 of messages while the non-reasoning tier never exceeds 0.005. The capability is present but goes unexercised unless asked for, locating the failure in propensity rather than competence. A decoder ablation shows the finding is recoverable only when the receiver reads the sender's stated number: an embedding-only decoder mis-reads the same data as near-babbling.

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