"Spending fifteen seconds to walk back and press the power button on the fridge seems like very inexpensive insurance to me. (OK, it's maybe 30 seconds, since it also should be turned back on afterwards.)"
But wouldn't you have to stop somewhere prior to getting to the fueling station (cuz others are fueling at the station), turn off propane, move to fueling station, fuel up, move to safe parking area away from fueling station, restart propane then move on? Seems like way to much effort for VERY slight chance of any thing happening.