Nova Kool refrigerators and freezers as installed in an Airstream Interstate run on either 120vAC or 12vDC, if the installer didn't make a mistake.
When any 120vAC source is available, the units default to that. The only way to make them run on 12vDC is to remove all 120vAC sources, including the inverter.
Running the units on the inverter is a waste. The fridges are designed to run on 12vDC, and include their own converter to convert incoming 120vAC to 12vDC; that's how they're able to operate AC/DC in the first place. So when you're using inverter power, you're turning 12vDC at the batteries to 120vAC to power the fridge/freezer, only to have the fridge/freezer convert it back to 12vDC. Since there are power losses at each device, the units operate less efficiently off the inverter than they do off straight DC power.
Seems to me that Airstream should
have plugged them into a 120vAC outlet that is not
powered by the inverter. That way it would run off 120vAC if you're on generator or shore power, but not off the inverter. On the non-Grand Tour models, some owners have unplugged the 120vAC cord to use their fridges in 12vDC mode only. This is a worthwhile modification for anyone who intends to boondock in their Interstate.
On the Grand Tours, that have separate fridges and freezers, there have been some
reports of the 12vDC connections accidentally being left undone at Jackson Center so the unit is installed as 120vAC only. If yours doesn't work on 12vDC, that is something that needs to be corrected.
One final note, if you shut off both the 12v
power and the inverter, the fridge and freezer will not
Does that clarify things, or just make them more confusing?