QCD sum rules are analytic predictions of hadron observables from quantum chromodynamics. In the so-called local-duality limit of their Borel-transformed form, all nonperturbative contributions are encompassed by just a single quantity, an effective threshold beyond which, by assumption, all hadronic contributions are reliably described by perturbative QCD. Reconstructing its quark-mass dependence enables us to investigate the differences of the leptonic decay constants of heavy--light mesons effectuated by the tiny isospin-violating discrepancy of the masses of up and down quarks. By and large, our findings enjoy excellent agreement with the outcomes of earlier studies, the only exception being a lattice-QCD prediction for the $B$ mesons, where we find dramatic disagreement.