Inference-time scaling can amplify reasoning pathologies: sycophancy, rung collapse, and premature certainty. We present RAudit, a diagnostic protocol for auditing LLM reasoning without ground truth access. The key constraint is blindness: the auditor evaluates only whether derivation steps support conclusions, enabling detection of trace-output inconsistency and, when latent competence exists, its recovery. RAudit measures process quality via CRIT-based reasonableness scores and varies critique formulation to study how social framing affects model response. We prove bounded correction and $O(\log(1/ε))$ termination. Experiments on mathematical reasoning (CAP-GSM8K) and causal judgment (CausalL2) reveal four mechanisms explaining model unreliability: (1) Latent Competence Suppression, where models derive correct answers then overwrite them under social pressure; (2) The False Competence Trap, where weaker judges mask sycophancy that stronger judges expose; (3) The Complexity-Vulnerability Tradeoff, where causal tasks induce more than 10 times higher sycophancy than mathematical tasks; and (4) Iatrogenic Critique, where authoritative correction harms weaker models. These findings challenge assumptions that capability implies robustness and that stronger feedback yields better outputs.