Automated detection of errors in clinical documentation is a promising application of large language models (LLMs), yet decisions to deploy such models rest on benchmarks that evaluate each clinical note in isolation. Error-detection benchmarks are typically constructed by injecting errors into notes, such that each erroneous note has a natural counterpart. Aggregate discriminative metrics (e.g., balanced accuracy or F1) do not exploit this structure. We show that this omission is consequential. In particular, evaluating 15 diverse LLMs on 4 standardized clinical error-detection test sets across 3 languages, we find that 13 of 15 models fall below the level of random pairwise discrimination, even while achieving F1 scores that standard practice would read as moderate. We also observe that the underlying bias patterns differ across languages: the same model can default to "no error" on one language and over-flag errors on another. To diagnose where discrimination breaks down, we further introduce a procedure to score the evidence models cite in their outputs. We find that while models consistently locate error-relevant content, they fail to produce the corresponding correct verdict on the clean counterpart. Finally, we show that F1 and pairwise accuracy are driven in opposite directions by the same underlying bias, so that ranking models by F1 may systematically promote the weakest discriminators. For safety-critical clinical NLP applications, we advocate for supplementing aggregate metrics with paired evaluations in benchmark reporting. Code and analysis scripts are available at https://github.com/healthylaife/paired-clinical-eval.

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