In physics, you should get the same result whichever way you calculate. As long as you do not make an error in calculations.
Calculating the greenhouse effect using radiative transfer equation, we get a result pretty close to the observed one, even if we neglect effects such as turbulent heat fluxes as long as we get Planck optical depth right. And this is why I think, even without following their derivation, that they must have made a massive error.
Another reason for that is simple intuition that airless (shortwave) albedo must me unimportant on planets with large optical depths (thick clouds) because at the surface you do not have much shortwave (solar) radiation anyway. The surface is dominated by longwave radiation (IR) which albedo is close to 0.0, anyway.