Rule-based reasoning, as in eligibility checks and contract reviews, requires language models to assess evidence against individual conditions and combine their judgments under explicit rules. Errors in evidence assessment can leave a decision unchanged, but misinterpreting or overlooking decision-critical evidence can reverse it. Identifying such evidence allows more capable models to focus on checking the corresponding condition judgments, supporting accurate and safe decisions. Recognizing the evidence's criticality requires understanding how evidence affects a condition judgment and how that judgment affects the decision. To achieve the goal, we propose a INTERvention-based imPACT learning framework (InterPact), which enables counterfactual verification of evidence criticality in rule-governed decisions. Specifically, its evidence intervention constructor generates training pairs for a propagation verifier by editing case facts with a frozen language model while holding rules and non-target conditions fixed. Human-reviewed labels record the resulting condition and decision changes, while complete state-to-decision mappings supervise consequences beyond the observed edit. During training, the verifier weights learned conditional decision predictions by evidence-based condition probabilities through a fixed composition operation, propagating decision-change supervision into the base model. At inference, the trained base model directly judges criticality from the original case and target evidence, without human or stronger-model supervision. On single-case evidence criticality verification over adapted rule-governed decision cases, InterPact achieves 68.28% accuracy, outperforming all six baselines. These results support learned decision sensitivity as a basis for prioritizing evidence checks.

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