  Recent optical studies in c-axis oriented superconducting MgB$_2$ films
indicate that the electron-phonon coupling is weak [tu01]. We reinforce this
conclusion by examining the raw reflectance data; its frequency dependence is
incompatible with strong electron-phonon scattering. This is further
strengthened by analysis of the real part of the conductivity, and by the
temperature dependence of the effective Drude scattering rate. Using a
realistic electron-phonon spectral shape [kong01], we find $\lambda_{\rm tr}
\approx 0.15$, in agreement with Tu et al. [tu01]. To the extent that
$\lambda_{\rm tr} \approx \lambda$, this disagrees sharply with model
calculations [kong01,kortus01,an01], and is far too low to provide the means
for $T_c = 39 $ K. A simple model is constructed with coupling to a high
frequency excitation, which is consistent with both the low frequency optical
data and the high $T_c$.
