As LLM agents are increasingly deployed in high-stakes enterprise settings, understanding how they handle sensitive information in agentic dialogue has become critical. Privacy leakage in such settings requires reasoning about whether information flows respect the contextual norms under which they originated. We extend CIMemories to CIMEMORIES DIALOGUE, a benchmark of 4,410 two-agent dialogue instances grounded in Contextual Integrity theory. Using this benchmark, we systematically evaluate 7 open-weight models from the Qwen3 and Llama 3.1 families across conversation lengths of 1 and 6 turns under three prompting conditions. We find that task capability and privacy leakage are fundamentally coupled: more capable models are systematically leakier, with no model in our evaluation able to decouple the two. Thinking models consistently leak more than their non-thinking counterparts, a pattern we attribute to the extended reasoning surface created by chain-of-thought. Leakage compounds with conversation length, rising up to 3x from 1 to 6 turns. Our results suggest that the coupling between task capability and privacy leakage is not an artifact of misconfiguration but a structural feature of current agentic systems.

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