  Recently, it has been proposed that a mechanism for the appearance of
non-equilibrium superconductivity in a resonantly driven semiconductor with
repulsive interband interactions exists.~\cite{Goldstein_PRB15} The underlying
microscopic model relies on the appearance of a specific fermionic dissipation
mechanism and the careful simultaneous tailoring of the electronic dispersion
relation and electron-electron interactions. We, instead, show that the
phenomenon is rather general and does not need a special fine tuning of
parameters. By considering a pair of bands with locally the same sign of
concavity, we demonstrate that interband pairing arises under the natural
assumption of the presence of phononic baths and radiative recombination. In
light of these findings, we demonstrate how the emergence of superconductivity
can be understood in terms of standard equilibrium interband BCS theory.
