I do shut off the fridge when fueling up (excepting the odd time I forget to do so). It's the law in most places, as it does have an open flame, per the fire marshal's definition of an open flame.
I also have smoke detectors in my house and RV, even though I've never had a house fire and they do go off with false alarms from time to time due to cooking, steam from a shower, dead batteries, etc. The chances of a house fire are relatively slim, like the chances of a gas station fire from an operating fridge, but why take unnecessary chances?