Organizations increasingly use oversight loops where one large language model (LLM) audits another's outputs alongside procedural traces of claimed steps. A common concern about such LLM-as-a-judge pipelines is that detailed traces make overseers gullible. Using signal detection theory, we audit five LLM overseers on 19 compliance tasks (4,551 analyzed judgments), varying only trace detail and evidence labeling. With disconfirming evidence always visible, error detection remains near ceiling. Instead, elaborate traces shift the decision criterion toward rejection, increasing false alarms in susceptible overseers. Without option labels, human-validated reason coding shows about 60% of false alarms cite an inability to tie evidence to its option. Labels eliminate this stated reason, yet residual rejection of correct work persists in those overseers and rises with trace detail. Procedural traces thus act as governance artifacts that shape oversight decisions. AI auditors should be evaluated by their decision criterion and false-alarm behavior, alongside accuracy.

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