We show that the time corresponding to the peak of the segmental relaxation time distribution and the mean time of that distribution for the components of several miscible polymer blends are strongly affected by both chain connectivity and concentration fluctuations. These two measures of characteristic segmental relaxation times differ from the time corresponding to the mean composition experienced by a segment, with these differences being emphasized for blends with large glass transition contrast, lower temperatures, or increased concentration fluctuations on the nanometer scale. These findings are in contrast to self-concentration models, which generally assume that concentration fluctuations affect neither the mean nor the peak segmental relaxation times and are only relevant for determining the distribution of relaxation times. Going further, we show through the inclusion of self-concentration and concentration fluctuation effects that segmental dynamics are only affected by a local environment of size similar to 1 nm surrounding a test monomer. This length scale is only weakly temperature and composition dependent, even near T-g. This estimate of a relevant dynamic length scale is in good agreement with the conjecture on which the Lodge-McLeish self-concentration model is based but is contrary to the ansatz used by many concentration fluctuation-based models which assume that this local environment size diverges in the vicinity of the glass transition.