My assertion is that a model of the form P(R|G,T) is always going to be more accurate than a model of the form P(R|T) alone - you can't gain anything by throwing away the G variable.

That's all true (modulo the objection about overfitting). However, there is the case where T affects G which in turn affects R. (Presumably this doesn't apply when T = treatment and G = gender). If what we're interested in is the effect of T on R (irrespective of which other variables 'transmit' the causal influence) then conditioning on G may obscure the pattern we're trying to detect.

(Apologies for not writing the above paragraph using rigorous language, but hopefully the point is obvious enough.)