We performed detailed photoluminescence (PL) spectroscopy studies of three different types of single-walled carbon nanotubes (SWNTs) by using samples that contain essentially only one chiral type of SWNT, (6,5), (7,5), or (10,5). The observed PL spectra unambiguously show the existence of an emission sideband at ∼140 meV below the lowest singlet excitonic (E11) level, whose identity and origin are now under debate. We find that the energy separation between the E11 level and the sideband is independent of the SWNT diameter within our experimental certainty. Based on this, we ascribe the origin of the observed sideband to coupling between K-point phonons and dipole-forbidden dark excitons, as recently suggested based on the measurement of (6,5) SWNTs.