Accidents can happen in most any kind of situation.
I see the videos on the local news quite often where someone is filling up their gas tank at the gas station, they get inside there car for a moment while the gas is pumping, get back out of the car, and go touch the gas nozzle to remove it. POW ! Just a spark from static electricity.
Driving with the propane on or off is going to be a personal thing. This is something that each customer will have to decide on.
I would think it is always going to be safer to leave the propane off while traveling, but if used properly and you are careful, it can be OK to leave it on while driving too.
If you are just running the refrigerator while driving, there are a few safety measures in place to help reduce any fire or explosion accidents.
1. If the pilot light on the refrigerator blows out for some reason while you are driving, the propane will automatically shut off to the refrigerator.
2. If you did get in a bad accident and the propane tank somehow flew out of the camper, ripped the connection hose off, and ripped the regulator out, the propane coming out of the tank will be very small. When the hose is not connected to the propane tank, I don't think any propane will come out on the newer style tanks. And in the newer connection hoses there is a small check valve that should close / reduce the propane flow if there is a big leak in the system.
Stuff happens.
People blow their BBQ's up all the time.
Houses catch fire.
There are car accidents.
Just be careful out there and have your safety measures in place.
(example: fire extinguisher, smoke detector, propane sensor, carbon monoxide sensor, etc, etc.)
One of my family members is a fire fighter. When I went to their house over the holidays I noticed a weird smell in the house? It smelled like an RV furnace (propane). They live in the country so their house is hooked up to a large propane tank for the gas supply. I asked ... "do you have any carbon monoxide sensors or propane detectors in the house?" The reply ... "huh? I don't think so". I did a quick room check and didn't see any. And looking at some of the smoke detectors, the batteries were removed! ARG!!!
Common sense is not so common these days.
.
.