The microscopic dynamics of hydration water exhibits some universal features that do not depend on the nature of the hydrated surface. We show that the hydration level dependence of the dynamic transition in the mean squared atomic displacements measured by means of elastic neutron scattering is qualitatively similar for hydration water in inorganic and organic hosts. The difference is that the former are 'rigid', whereas the dynamics of the latter can be enhanced by the motions of the hydration water. The overall hydration level appears to be the main parameter governing the magnitude of the mean squared atomic displacements in the hydration water, irrespective of the details of the hydrated host.