  The $SU(3)$-violating decays $\Phi^{2S} \goto \Phi^{1S} X$, where $X = \pi^0$
or $\eta$ and $\Phi = J/\psi$ or $\Upsilon$ have been recently proposed as a
means of probing the light quark masses beyond leading order in chiral
perturbation theory. We argue that this analysis is incorrect, even in the
heavy quark limit. We show that these decays are governed by an infinite number
of matrix elements which are not suppressed by any small parameter, and which
cannot be computed with our present understanding of QCD. Furthermore, for
sufficiently heavy quarks, we show that the decay amplitudes can be organized
into a twist expansion, and that the contributions considered in the above
proposal are subleading in this expansion. We also explain how these decays
nonetheless give a constraint on the light quark masses valid at {\it leading
order} in the chiral expansion. The decays $\Phi^{1S} \goto \eta\gamma$ and
$\Phi^{2S} \goto \Phi^{1S} \pi\pi$ also have contributions from infinitely many
operators, contrary to claims in the literature.
