We compute the O(alpha_s^2) correction to the decay rate eta_c --> gamma
gamma and discuss its implications for precision quarkonium physics. We study
the suitability of the ratio Gamma(J/psi --> e+e-)/Gamma(eta_c --> gamma
gamma), in which the non-perturbative or soft effects cancel at
O(alpha_s^{0,1}), for extracting fundamental parameters of QCD at low energies.
We show that the QCD-based theory of charmonia is not capable of predicting
this ratio with any degree of confidence.Comment: 6 page