Tens of thousands of rotation periods have been measured in the Kepler fields, including a substantial fraction of rapid rotators. We use Gaia parallaxes to distinguish photometric binaries (PBs) from single stars on the unevolved lower main sequence, and compare their distribution of rotation properties to those of single stars both with and without Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectroscopic characterization. We find that 59% of stars with 1.5day<P<7day lie 0.3mag above the main sequence, compared with 28% of the full rotation sample. The fraction of stars in the same period range is 1.7{+/-}0.1% of the total sample analyzed for rotation periods. Both the PB fraction and the fraction of rapid rotators are consistent with a population of non-eclipsing short-period binaries inferred from Kepler eclipsing binary data after correcting for inclination. This suggests that the rapid rotators are dominated by tidally synchronized binaries rather than single stars obeying traditional angular momentum evolution. We caution against interpreting rapid rotation in the Kepler field as a signature of youth. Following up on this new sample of 217 candidate tidally synchronized binaries will help further understand tidal processes in stars.