Fidelity metrics, such as per-token KL divergence (KLD) against a high-precision reference, are often used in practice as low-cost proxies for benchmark quality. We test this practice on a 28-quant cohort of Qwen3.6-35B-A3B and a 41-quant cohort of Devstral-Small-2-24B, evaluated across a suite of downstream benchmarks. We find that KLD is strongly correlated with benchmark score over the full cohort (
ρ=−0.72 on Qwen and
ρ=−0.86 on Devstral, both with
p<0.001). However, this relationship collapses to non-significance in the near-baseline silent zone (
ρ=+0.00 on Qwen and
ρ=−0.24,
p=0.36, on Devstral). This collapse persists across 14 measurement variants, including different KLD aggregations, perplexity formulations, top-1 agreement, calibration corpora, and context lengths. At the per-prompt level, KLD has only weak failure-prediction power on code, with failed-vs-passed geometric-mean ratios in
[1.08,1.22] across five models on LiveCodeBench, and fails as a cross-model router, achieving only
42.3%−49.4% accuracy on disagreement prompts. We trace the collapse to a structural decomposition: KLD primarily measures the volume of disagreement with the reference, with silent-zone composite
ρ=+0.94 (
p<0.001) on Qwen and
+0.55 (
p=0.03) on Devstral, while its relationship to the direction of those disagreements is weak and task-conditional.