Self-distillation for grounded question answering often filters tutor trajectories with agreement or confidence gates. For such gates to support faithful grounding, their signals should depend on the supplied document rather than on answers recoverable from parametric memory. We propose a four-mode randomization-control diagnostic that applies the same frozen gate to original, randomized, irrelevant, and empty documents for the same question. On HotpotQA and MuSiQue, using Qwen2.5-7B-Instruct with eight tutor traces, the joint gate changes sharply with document condition: kept fraction falls from 0.380 to 0.020 and from 0.330 to 0.015, respectively. Randomized and irrelevant documents lie between the endpoints, while a document-blind random gate stays flat. The protocol audits document sensitivity without additional student training; faithful evidence use and downstream gains require separate validation.