Old guy, did you mean to say propane tank off instead of fridge off when traveling?
Question; excuse my ignorance I'm new to this and haven't yet had to refill the propane tank on my DP, but comments on this thread indicate the propane tank shutoff valve should be OFF when refilling. I'm thinking of my home BBQ tank and you can't refill the 20lb portable tank without opening the valve. There must be another way on the coach propane tank.
Incidentally turning off the propane tank is on my campground departure checklist. The fridge uses the inverter with the batteries recharged by the engine alternator. It just makes sense to me not to have pressurized propane in the pipes throughout the coach when traveling 60 mph.