Evidence-based medicine demands strict logical consistency, yet current evaluations of large language models (LLMs) prioritize superficial label matching over genuine reasoning. We introduce LogiMed-RoB, a benchmark grounded in Cochrane Risk of Bias (RoB) 2.0 expert logic, comprising 860 randomized controlled trials (RCTs) and 14,820 queries. It evaluates models under the Hierarchical Logical Consistency (HLC) framework across four dimensions: Atomic Consistency, Domain Consistency, Aggregation Consistency, and Evidential Faithfulness. Experiments on 10 state-of-the-art LLMs reveal a catastrophic Error Compounding Effect: despite the top model reaching 98.88% Atomic Consistency, its end-to-end consistency collapses to 45.13%, with several open-weight architectures plummeting to nearly 0%. We further uncover a systematic evidence-reasoning gap: even when models retrieve high-quality evidence, they fail to deduce correct outcomes in 18.63-40.05% of cases, while Blind Guess Rates reach 48.28%. LogiMed-RoB demonstrates that high outcome accuracy can conceal critical reasoning flaws, underscoring the necessity of white-box logical verification for clinical deployment.

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