Addendum to “Possibility of 0-$g$-factor paramagnetic molecules for measurement of the electron's electric dipole moment”

Recent experimentation has revealed a discrepancy between the calculated and actual hyperfine structure of the ${}^{207}$Pb${}^{19}$F molecule. This discrepancy has been attributed to a misrepresentation of the parity for the ground-state PbF molecule. In a previously published work [Shafer-Ray, Phys. Rev. A 73, 034102 (2006)], we derived a formula for the electric-field-dependent $g$ factor of the ground-state PbF molecule with the misassigned parity. In this Addendum, we reformulate that work and derive the $g$ factor based on the corrected ground state. We discuss the impact of the corrected $g$ factor of the PbF molecule and conclude that the PbF molecule has a $g$ factor which can be small enough to perform an experiment sensitive to the electron's electric dipole moment.