Classical Wolf-Rayet stars are evolved, hydrogen depleted massive stars that exhibit strong mass-loss. In theory, these stars can form either by intrinsic mass loss (stellar winds or eruptions), or via mass-removal in binaries. The Wolf-Rayet stars in the Magellanic Clouds are often thought to have originated through binary interaction due to the low ambient metallicity and, correspondingly, reduced wind mass-loss. We performed a complete spectral analysis of all known WR binaries of the nitrogen sequence in the Small and Large Magellanic Clouds, as well as additional orbital analyses, and constrained the evolutionary histories of these stars. We find that the bulk of Wolf-Rayet stars are luminous enough to be explained by single-star evolution. In contrast to prediction, we do not find clear evidence for a large population of low-luminosity Wolf-Rayet stars that could only form via binary interaction, suggesting a discrepancy between predictions and observations.