We analyze the effect of companion stars on the bulk density of 29 planets orbiting 15 stars in the Kepler field. These stars have at least one stellar companion within 2, and the planets have measured masses and radii, allowing an estimate of their bulk density. The transit dilution by the companion star requires the planet radii to be revised upward, even if the planet orbits the primary star; as a consequence, the planetary bulk density decreases. We find that, if planets orbited a faint companion star, they would be more volatile-rich, and in several cases their densities would become unrealistically low, requiring large, inflated atmospheres or unusually large mass fractions in a H/He envelope. In addition, for planets detected in radial velocity data, the primary star has to be the host. We can exclude 14 planets from orbiting the companion star; the remaining 15 planets in seven planetary systems could orbit either the primary or the secondary star, and for five of these planets the decrease in density would be substantial even if they orbited the primary, since the companion is of almost equal brightness as the primary. Substantial follow-up work is required in order to accurately determine the radii of transiting planets. Of particular interest are small, rocky planets that may be habitable; a lower mean density might imply a more volatile-rich composition. Reliable radii, masses, and thus bulk densities will allow us to identify which small planets are truly Earth-like.
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