We examine correctness‑gated multi‑teacher distillation in a fixed experimental matrix. Eight arms share 4,330 source examples, a 63.9M‑parameter student, 12,990 optimization rows, 406 updates, evidence inputs, and a decoder. Seven teacher‑based arms use a single fixed three‑response pool, and three random seeds are evaluated on 267 held‑out examples.
Compared with unfiltered distillation, the correctness‑weighted arm improves accuracy by $+0.1660$ (95% observed interval $[0.0670, 0.2455]$), macro‑F1 by $+0.1323$ ($[0.0916, 0.1731]$), and reduces the task‑defined conditional unsafe‑action rate by $-0.4979$ ($[-0.5926, -0.3686]$). These shifts do not imply uniformly better behavior. Source‑label SFT achieves the highest mean macro‑F1 ($0.586$). The weighted arm records zero Refuted recall in every seed, and two seeds label all 167 claim examples as NotEnoughInfo.
In an availability‑amended audit on one reference seed, weighted and unfiltered outputs yield evidence‑supported positives $0/20$ vs $1/20$, and positives containing unsupported material $20/20$ vs $19/20$. Samples are non‑paired, source overlap is not serialized, and the amendment follows automatic summarization but precedes annotation, preventing estimation of a common‑source grounding effect. Consequently, the audit cannot determine system‑level improvement or harm.
Hard filtering already attains $0.660$ accuracy, $0.530$ macro‑F1, and $0.135$ conditional unsafe rate. The implemented weighted arm shows no demonstrated incremental decision benefit over hard filtering. This fixed‑matrix failure analysis reveals decision redistribution with lost label functionality, and the available human audit does not establish a grounding gain.
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