"An infrared camera (right image) shows how a sample of the whitest white paint (the dark purple square in the middle [of the infrared image]) cools the board below ambient temperature." So... Maxwell's demon?
Well, if something can only radiate, and will absorb much less than it radiates... the only way it could stay at ambient temperature would be via contact transmission. I would expect an object painted in this whitest paint to cool below ambient temperature unless it had a heater inside it, say, or unless it was submerged in water rather than air.
The process of electromagnetic radiation is the inverse of electromagnetic absorption, and so what will happen here is that the sample will reach a state of thermal equilibrium with the walls of its container (or the 2.7K cosmic background radiation if we're in deep space) through the exchange of infra-red radiation. If it went to a lower temperature, we could create a perpetual motion machine by putting a thermocouple between the painted object and its container.
It is possible to cool some things with radiation, but that requires creating a state that is not in thermal equilibrium, which is not plausible for paint on a wall.