It absolutely does matter, because the beads that are tuned to radiate particular frequencies of infrared will also be tuned to absorb those frequencies as well. If the frequencies aren't transparent to the atmosphere, you'll be reabsorbing just as much as you transmit and end up at equilibrium with the atmosphere.
It is essentially similar to the way in which you can freeze water in a shallow dish on clear nights that are nonetheless slightly above freezing temperature - you are facing a black-body radiator that is well below ambient local temperature.
That's a great explanation. I wish the article had put it in these terms... because reading through it, I kept thinking there was no way to cool the building to below the ambient temperature. But if you're equilibrating with space instead of the atmosphere, that's a whole different kettle of fish.
At night sure, in the day time the sun is adding heat across a wide band of frequencies. This heats up less, but does not drop below ambient temperature in full sunlight.
The advantage of targeting the IR window is that it would work even with clouds and water vapor in the atmosphere whereas, plain old thermal radiation needs a clear night to be effective.
Of course it won't pump heat backwards into the sun but they propose a water circulation system, which I imagine could store some daytime heat to release it at night. That and masonry of the walls of the building would store even more.
It is essentially similar to the way in which you can freeze water in a shallow dish on clear nights that are nonetheless slightly above freezing temperature - you are facing a black-body radiator that is well below ambient local temperature.