Cigarette lighter sockets were invented and began to appear in cars in the 1920s. The cigarette lighter gets pushed in, gets hot, and the socket pops it out. If it is jammed and can't pop out the socket protects the car from a fire by causing an open circuit. There are two ways to do this. One way (I've seen it in Fords) is the socket senses the heat and causes a short circuit blowing the fuse. When it cools down the short goes away. The other way (I've seen it in GMs) is to have a fuse like wire in the socket that is exposed to the heat and melts when there is too much current or too much heat.
The point of the socket is to pop out and provide fire protection. When you plug a fridge into a cigarette lighter socket the friction holding it in is not much. It can pop out from vibration. As it gets loose the contact between the center of the plug and the center of the socket will have resistance. The 3 or 6 amps the fridge needs isn't enough to overload the circuit and blow the fuse. It is enough to generate significant heat with the center contact being loose. That heat can trigger the socket protection mechanism.
Power sockets that do not work with cigarette lighters but still work with center contact plugs usually don't have a protection mechanism. Often the fuse located in the tip of the plug will get hot enough to blow even though the current isn't too high. The heat from resistance of the bad contact melts the fuse wire.
Bottom line, it's the socket not the kettle. I use a 2 burner propane camp stove to heat the water and and an Aeropress to make the coffee. I got the 2 burner stove because it is low, flat, wide, and very stable. The butane and propane singles seem to me to be tippy and likely to heat the fuel supply.