Quark-hadron duality and the determination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> from hadronic <mml:math xmlns:mml="http://www.w3.org/1998/Mat

Nonperturbative effects have a small but nontrivial impact on the determination of the strong coupling from hadronic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>τ</a:mi></a:math> decay data. Several approaches have been proposed to take these into account, the two most important of which are the “truncated Operator Product Expansion (OPE)” approach and “Duality Violation (DV)-model” approach. Recently, Pich and Rodríguez-Sánchez have raised a number of criticisms of the latter approach, including, most notably, claims of the existence of (i) a supposed instability with respect to variations of the model for incorporating quark-hadron duality violations, and (ii) an alleged redundancy in the fitting strategy employed in the DV-model approach. In this paper, we investigate these criticisms and show they fail to survive more detailed scrutiny of the mathematical or numerical arguments that underpin them. We also show that, while the redundancy claim does not apply to the DV-model approach, it does, in fact, apply to the truncated OPE approach. In particular, the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>α</c:mi><c:mi>s</c:mi></c:msub></c:math> value determined in the latter turns out to derive purely from perturbation theory, with no role played by the nonperturbative condensates determined in the rest of the analysis. This leads to the conclusion that a revision of the conventional understanding of what is learned from truncated OPE analyses is necessary and that only very limited self-consistency checks are possible within this framework. These observations raise new, nontrivial issues for the truncated OPE approach.