Test-time scaling methods implicitly assume that additional computation from the same model provides independent evidence. We show that this assumption fails within a single reasoning model: errors are correlated across repeated samples, across reasoning depth, and in the model's own self-evaluation, so more compute from the same model is not more evidence. We introduce DIA (Disagreement-triggered Independent Arbitration), which treats disagreement between an intermediate-stage and the final-stage prediction as a per-question signal of reasoning instability and resolves it by asking a small panel of heterogeneous models to solve the question independently, without seeing either candidate, and aggregating their answers directly. Across seven benchmarks and two base models, DIA outperforms full chain-of-thought in 12 of 14 settings, including a 7.00% gain on MuSiQue, while activating on only $\sim 17\%$ of examples and using up to 47.2% fewer tokens than a multi-agent baseline. Ablations show that both independent solving and solver heterogeneity are necessary for these gains.

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