The inflection frequency of the deuteron magnetic relaxation dispersion from water in rotationally immobilized protein samples has recently been found to be essentially independent of temperature and protein structure. This remarkable invariance has been interpreted in terms of a universal residence time of 1 microseconds for protein-associated water molecules. We demonstrate here that this interpretation is an artifact of the conventional perturbation theory of spin relaxation, which is not valid for rotationally immobile proteins. Using a newly developed non-perturbative, stochastic theory of spin relaxation, we identify the apparent correlation time of 1 microseconds with the inverse of the nuclear quadrupole frequency, thus explaining its invariance. The observed dispersion profiles are consistent with a broad distribution of residence times, spanning the microseconds range. Furthermore, we argue that the deuteron dispersion is due to buried water molecules rather than to the traditional surface hydration previously invoked, and that the contribution from rapidly exchanging protein hydrogens cannot be neglected. The conclusions of the present work are also relevant to proton relaxation in immobilized protein samples and to magnetic resonance imaging of soft tissue.