Does radiating heat to outer space through the atmospheric transparency window have any impact on heat loss? I was reading this article: Passive radiative cooling below ambient air temperature under direct sunlight
The authors are improving upon the age-old idea of reflecting incoming sunlight while radiating heat away. The point that I don't get is why do they need to meet this criteria:

...radiate heat to outer space through a transparency window in the
  atmosphere between 8 and 13 micrometres.

They also state that

Further, the cold darkness of the Universe can be used as a renewable
  thermodynamic resource, even during the hottest hours of the day.

Further in the article they do not elaborate on why specifically they need to use the outer space as a heat sink. The equations don't imply anything about that.
The only way I can figure out this being useful is not heating the atmosphere and preventing the heat from being trapped at all, radiating it away from Earth, thus combating global warming. The fact that the apparatus is using outer space as a heat sink or just using the atmosphere should not have any significant impact on radiative cooling properties. Is this reasoning correct?
 A: Short answer: For their heat sink they choose outer space (-270 °C) instead of the atmosphere (avg. near surface = 17 °C) for the simple reason  that space is much colder as Anna V points out. If the cooler didn't emit through the atmosphere's transparency window, the cooler would also absorb extra radiation from the atmosphere and warm up due to Kirchhoff's law of thermal radiation: "a body emits radiation at a given temperature and frequency exactly as well as it absorbs the same radiation."
That's why the graph of cooler emissivity/absorptivity from the paper is labeled as such-- they are equivalent:

Say instead of aiming for the transparency window they designed the cooler to emit at frequency $X$ that the atmosphere does absorb. By Kirchhoff's law of thermal radiation, since the atmosphere absorbs at $X$ it also emits at $X$. And likewise since the cooler emits at $X$ it also absorbs at $X$. That would result in the cooler absorbing more radiation from the warm atmosphere overall which would heat it up.
A: 
The fact that the apparatus is using outer space as a heat sink or just using the atmosphere should not have any significant impact on radiative cooling properties. Is this reasoning correct?

No, it is not. The cooling properties of the apparatus depend on the heat sink to which the heat is aimed, as the final result will be an equilibrium of apparatus/environment . If the heat sink is the atmosphere the apparatus can only cool down to the atmosphere's temperature. As the temperature differential with outer space is enormous equilibrium will not be reached and the apparatus will keep cooling. The aim of the apparatus is to reduce the heat content of the earth system by transferring it radiatively to space.
