Confidence is not competence: Inverse-folding models know binding in the mixed derivative

Staged binder design generates a backbone and then inverse-folds a sequence, where current approaches read the model's confidence to judge interface choices. Recovery-based evaluations report a hotspot deficit taken as evidence that inverse-folding models cannot place binding-critical residues. We show this metric is misaligned with binding competence: while confidence evaluates the likelihood within a single bound state, competence requires comparing likelihoods across bound and unbound states, making confidence the wrong proxy for binding. Confidence is a within-state scalar of the bound-conditioned distribution $P$. Binding leverage is the mixed second derivative, the response to ablating the partner, which has the form of the model's classifier-free-guidance direction. Leverage is not determined by $P$, so every scalar of confidence is blind to it by construction. On SKEMPI natural complexes, confidence ranks hotspots near chance, whereas the mixed derivative, a zero-shot readout, tracks experimental binding free energy (Spearman $-0.30$ pooled, $-0.21$ per interface) and adds signal beyond geometry, conservation, and the one-pass log-odds. The effect holds across four architectures and beyond a fitted physics function (FoldX). But the advantage is regime-specific: on de-novo designed binders confidence overtakes it (interface AUROC $0.61$ versus $0.57$). Nonetheless, the signal is actionable: a small logit tilt on a frozen ProteinMPNN raises binding-favorability. The tilt beats a random tilt broadly, and a same-magnitude confidence tilt out of family on FoldX (best-of-k, lower CI $+0.72$ kcal/mol), while ipTM measures foldability rather than binding. Separately, the reported deficit is itself largely a burial and composition confound. The recipe is not protein-specific: to read an untrained quantity from a conditional generative model, ablate its conditioner and take the mixed derivative. We test it only on proteins.