Physiological foundation models encode how a signal was recorded alongside the physiology it reflects. When recording conditions are associated with diagnosis, this acquisition provenance can become a shortcut, yet the usual evidence, shifted transfer and provenance decodability, does not show whether a predictor uses it. We introduce PhysioTRACE, a four-axis behavioral audit for frozen encoders that separates what a probe can decode from what a fixed task head relies on. Recover scores how decodable provenance is; Stress reverses only the provenance-target association on the same held-out records; Intervene removes a train-localized provenance component; and Verify certifies that removal only if it beats matched random projections within a declared utility margin. Each audit thus ends in one of three verdicts: no reliance, or reliance with the remedy certified or refused. Across EEG and ECG, five training objectives, and five frozen foundation models, the relation between Recover's calibrated score and out-of-distribution utility changes sign between datasets, so neither can stand in for a reliance test. On paired EEG views where the shortcut is known by construction, the audit detects it (the exposed head loses about 0.2 AUROC when the association is reversed, while a control head is unaffected) and certifies removal of a rank-two component that restores control-level behavior without measurable utility loss, for both encoder objectives tested. On real ECG device metadata it returns all three verdicts: it certifies a remedy that removes 91% of one model's excess vulnerability, finds no reliance where device and diagnosis are barely associated, and refuses the remedy for a second model whose localized direction also carries task signal. Robustness to how inputs were recorded therefore needs a behavioral test, and PhysioTRACE provides one that can pass, fail, or refuse a remedy.

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