We have studied the ¹⁵C(d,p)¹⁶C reaction in inverse kinematics using the Helical Orbit Spectrometer at Argonne National Laboratory. Prior studies of electromagnetic-transition rates in ¹⁶C suggested an exotic decoupling of the valence neutrons from the core in that nucleus. Neutron-adding spectroscopic factors give a different probe of the wave functions of the relevant states in ¹⁶C. Shell-model calculations reproduce both the present transfer data and the previously measured transition rates, suggesting that ¹⁶C may be described without invoking very exotic phenomena.