You repeated one of my own points back to me and then condescended down to me about not appreciating orders of magnitude. (I'm a physicist myself.) The whole purpose of my comment is that 25 is not that small of a factor on astronomical scales and it suggests the BB radiation of the planet itself would be detectable. As it turns out, this is the case

> As a result, [the planet] has an extremely high equilibrium temperature, assuming zero albedo and perfect heat redistribution, of ∼4050 K. This is as hot as a late K-type star, and thus we expected a large thermal emission signal, which we easily confirmed with our z'-band detection of the secondary eclipse with a depth of ∼ 0.1% (Figure 1). This measurement implies an even hotter day-side temperature of ∼ 4600 ± 150 K, likely indicating poor redistribution of energy to the night side of the planet and a temperature closer to that of a mid-K star.

https://arxiv.org/pdf/1706.06723

Note also that, contra your suggestion that the planet might just be too cold on night side to have significant BB radiation, the night-side temperature is only 15% lower than the mean.