Very common question- not dumb at all, and much discussed here and elsewhere. (As you can see from the immediately preceding post- Thanks, 2Oldman! :W )
Though hardly scientific "polls", it's interesting to observe that majority responses to this question tend to be in the affirmative. Usually by a wide margin most responders run the fridge on propane while traveling, though of course turning it off at gas pumps as with any other ignition source. It's also required to be shut down when on ferries, at least out here in Washington, and in some tunnels.