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In such cases, safe medical communication typically involves redirection: addressing the implicit misconception and then responding to the underlying patient context, rather than the original question. While large language models (LLMs) are increasingly being used by lay users for medical advice, they have not yet been tested for this crucial competency. Therefore, in this work, we investigate how LLMs react to false premises embedded within real-world health questions. We develop a semi-automated pipeline to curate MedRedFlag, a dataset of 1100+ questions sourced from Reddit that require redirection. We then systematically compare responses from state-of-the-art LLMs to those from clinicians. 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