In response to your questions: yes, it can in fact cool below the ambient air temperature entirely passively (even during the day! -- which adds real value for cooling applications). We've shown in other recent work that you can use this effect to cool as much as 45-50°C below the ambient air temperature, if you insulate the radiator perfectly.
The reason this works here on Earth is that some upward thermal radiation isn't absorbed and re-emitted back to you. So if you start at the air temperature, looking upwards, you will be sending more heat out than the sky sends back to you. This allows an upward-looking surface to cool itself down until the heat going out and coming back to it balance out.