Crystals containing Ni10 magnetic molecules display an unprecedented form of out-of-equilibrium behavior of the bulk magnetization M at temperatures as high as 17 K. We have performed 1H NMR measurements to probe the local Ni magnetic moments and their dynamics. It is apparent that no freezing of the Ni moments occurs, in striking contrast to what is observed in blocked superparamagnetic systems. The average local moments display the same behavior as M, thus unambiguously demonstrating the intrinsic character of the phenomenon. This result supports the hypothesis that the slowing down of M is due to a resonant phonon trapping mechanism which prevents the thermalization of M but not the fast spin flippings of the individual molecular moments. Indeed, the measured nuclear spin-lattice relaxation rate points to fast single-molecule dynamics at low temperature.