LLM agents that answer questions and act on behalf of users must decide when to yield to a user who disagrees. Disagreement may correct a genuine error or may be an attempt at manipulation. Prior work shows that models frequently abandon correct answers when challenged by users, yet it remains unclear whether they distinguish correction from manipulation or merely differ in their propensity to concede. We examine this question across seven LLMs from four vendors in two studies, one on the answers agents give and one on the actions they take as customer-support agents whose policy permits account changes only for verified users. Simulated users push toward correct and incorrect answers with graded pressure. Following research on epistemic vigilance, the pressure either appeals to the source, such as claimed authority, or offers content the agent cannot verify, namely a cited source. Drawing on signal detection theory, we measure on a set of benchmark questions how much more readily each agent concedes to correction than to manipulation, separately from its overall propensity to concede. Citations made five of seven models readier to concede and four worse at discriminating, while stronger wording added little. In the agentic study, five models never violated the verification policy, including models that readily abandoned correct answers, so concession on answers did not predict violations of policy. Ministral 3B violated the policy mainly under claimed authority, and Ministral 8B reported changes it had not made. An instruction to revise only on verifiable evidence chiefly shifted propensity to concede rather than improving discrimination. Concession rates alone are therefore misleading, and agents should be evaluated on both their discrimination and the actions they take.

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