Now, getting back to the very original question
While parked and top elevated, you can run the fridge in any power mode - provided this power is being provided.
BUT, and this is something that a I didn't previously understand, if the camper is closed - AND NOT UNDER TOW - the fridge will not receive adaquate cooling of its components. Running the fridge this way - in any mode - will compromise it.
Summerizing, as I understand it, if parked and elevated, you can use any power source. If closed and parked, no extended cooling use is advised. Very short time use (under one hour/ any power souce) is OK.
While under way, propane is NOT advisable and AC power is Not Applicable. Use DC power to keep things cool but do realize the power draw is significant on your tow vehicle and will slowly deplete your batteries.
I may be wrong but that's how I understand it.