  It has been suggested that the radiative $X \to D \bar D \gamma$ decay modes
are useful to shed light on the structure of the meson X(3872), since the ratio
$ R={\Gamma(X \to D^+ D^- \gamma) \over \Gamma(X \to D^0 \bar D^0 \gamma)}$ is
expected to be small ($R \ll 1$) if $X$ is a molecular $D^{*0} \bar D^0$ state.
We compute $R$ in a $\bar c c$ $J^{PC}=1^{++}$ description of $X$ finding that
it is tiny in a wide range of hadronic parameters governing the decay. A
discrimination between the molecular and $\bar c c$ description can be obtained
through the analysis of the photon spectrum.
