Multiple-choice question (MCQ) benchmarks are widely used to evaluate large language models, yet a single reported accuracy number is not enough to distinguish a model's latent ability from order sensitivity. Debiasing methods tend to be judged on one axis, which implicitly assumes that fixing order sensitivity and improving accuracy go together. We test this assumption with two proprietary models and two open-weight models on MMLU and ARC-Challenge, across four families of strategies. We measure order sensitivity with flip rate, capturing per-question instability, and recall standard deviation (RStd), capturing aggregate positional imbalance. We find accuracy and order sensitivity do not move together consistently: two-stage prompting reduces both flip rate and RStd for GPT on MMLU without a significant change in accuracy. The two sensitivity metrics also diverge from each other. Adding reasoning to direct answering leaves Llama's MMLU flip rate statistically indistinguishable while RStd falls sharply. A $2\times2$ ablation across generation-then-matching, crossing option visibility with matcher type, shows that withholding options mainly harms semantic matching, which achieves zero flip rate by construction, yet loses significantly in accuracy; the effect is smaller when using an LLM matcher. We recommend reporting flip rate and RStd along with accuracy when evaluating MCQ strategies.

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