We analyze recent deuterium NMR data on blends of poly(ethylene oxide) (PEO) with poly(methyl methacrylate) (PMMA), using a model for the blend dynamics based on the coupling model. This model has previously been shown to describe the relaxation properties of blends whose component dynamics are strongly composition dependent. We show herein that the unusual feature of PEO/PMMA blends, an invariance of the PEO dynamics to composition, is a natural consequence of the high frequency and temperature of the NMR experiments. To wit, when the independent relaxation time of our model approaches the characteristic time for intermolecular cooperativity (similar to2 ps), the effect of local environment on the component dynamics becomes negligible. A similar situation pertains for poly(vinyl methyl ether) mixed with polystyrene, at temperatures sufficiently high that the segmental relaxation times become small. On the other hand, for blends of 1,4-polyisoprene with poly(vinylethylene), the component dynamics retain their dependence on composition, even at high temperatures. The reason for the differing behavior is brought out by an analysis using our blend model.