  Non-perturbative effects have a small but non-trivial impact on the
determination of the strong coupling from hadronic $\tau$ decay data. Several
approaches have been proposed to take these into account, the two most
important of which are the ``truncated OPE'' approach and ``DV-model''
approach. Recently, Pich and Rodr\'iguez-S\'anchez 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 address these criticisms one by one, showing 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. 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, non-trivial issues for the truncated OPE approach.
