Previous (CH4)-C-13/(C2H2)-C-12 isotopic competition experiments on the mechanism of diamond growth by chemical vapor deposition are reanalyzed in light of recent evidence for a nonlinear dependence of the first-order Raman shift frequency on C-13 mole fraction. The new Raman data imply a C-13 mole fraction for mixed-isotope diamond films several percent higher than that reported previously. The corrected carbon-13 mole fractions of polycrystalline diamond films and homoepitaxial films grown on (100), (111), and (110) natural diamond substrates were each equal, within experimental error, to that of the methane above the substrate but significantly different from that of gas-phase acetylene. As the C-13 mole fractions of methyl radical and methane should be nearly identical, the methyl radical is concluded to be the predominant growth precursor regardless of the crystallographic orientation of the diamond substrate.