Mossbauer spectroscopy and neutron scattering measurements on proteins embedded in solvents' including water and aqueous mixtures have emphasized the observation of the distinctive temperature dependence of the atomic mean square displacements, < u(2)>, commonly referred to as the dynamic transition at some temperature T-d. At low temperatures, < u(2)> increases slowly, but it assumes,stronger temperature dependence after crossing T-d, which depends, on the time/frequency resolution of the spectrometer. Various authors, have made connection of the dynamics of solvated proteins, including the dynamic transition to that of glass-forming substances. Notwithstanding, no connection is made to the similar change of temperature dependence of < u(2)> obtained by quasielastic neutron scattering when crossing the glass transition temperature T-g, senerally observed in inorganic, organic, and polymeric glass-formers. Evidences are presented here to show that such a change of the temperature dependence of < u(2)> from neutron scattering at T-g is present in hydrated or solvated proteins, as well as in the solvent used, unsurprisingly since the latter is just another organic glass-former. If unaware of the existence of such a crossover of < u(2)> at T-g, and if present, it can be mistaken as the dynamic transition at T-d with the ill consequences of underestimating T-d by the lower value T-g and confusing the identification of the origin of the dynamic transition. The < u(2)> obtained by neutron scattering at not so low temperatures has contributions from the dissipation of molecules while caged by the anharmonic intermolecular potential at times before dissolution of cages by the onset of the Johari-Goldstein beta-relaxation or of the merged alpha-beta relaxation. The universal change of < u(2)> at T-g of glass-formers, independent of the spectrometer resolution, had been rationalized by sensitivity to change in volume and entropy of the dissipation of the caged molecules and its contribution to < u(2)>. The same rationalization applies to hydrated and solvated proteins for the observed change of < u(2)> at T-g.