Chris Ho-Stuart says..
…..”A number of my co-authors did have degrees in physics, and specific expertise in thermodynamics. No great expertise was actually needed. A competent undergraduate comprehension is more than enough.”…
I would agree with that.
Backradiation (as you call it) does exist.
However it is not heat.
Heat has the capacity to be turned into work in the given situation.
In a purely radiative exchange heat would be the net value of the radiative flows.
I guess that your physics co-authors had not brushed up recently on their undergraduate thermodynamics.
Its the only charitable excuse I can think of.