While addition of electrolyte to sodium dodecyl sulfate suspensions of single-wall carbon nanotubes has been demonstrated to result in significant brightening of the nanotube photoluminescence (PL), the brightening mechanism has remained unresolved. Here, we probe this mechanism using time-resolved PL decay measurements. We find that PL decay times increase by a factor of 2 on addition of CsCl as the electrolyte. Such an increase directly parallels an observed near-doubling of PL intensity, indicating the brightening results primarily from changes in nonradiative decay rates associated with exciton diffusion to quenching sites. Our findings indicate that a reduced number of these sites results from electrolyte-induced reorientation of the surfactant surface structure that partially removes pockets of water from the tube surface where excitons can dissociate, and thus underscores the contribution of interfacial water in exciton recombination processes.