I think the idea is that black holes can never shrink to a size small enough to emit a hawking radiation hotter than CMB as long as it receives photons from the CMB that that will balance the mass/energy of the black hole and keep it in equilibrium.

This obviously is not a problem if you create a new very small black hole from scratch as it only applies to pre-existing black holes that are massive enough so that their hawking radiation temperature is lower than the CMB