It seems implicit in the explanation of the Born-Oppenheimer approximation that the velocity of the nuclei is only determined by the Coulomb interactions. In that case, it makes sense that the electrons have little influence on the kinetic energy of the nuclei, given the mass difference. If, however, there are other factors that can influence the kinetic energy of the nuclei, this approximation may no longer be valid. Perhaps this could be the case if the solid is at a very high temperature of if it is subjected to radiation that energizes the nuclei.