the photo in the referenced article shows a plastic case badly damaged by heat. I agree that it could potentially start a fire but, from the description of the problem, I'd be surprised if if a bad plug caused this. I suspect that the melted item is part of the on/off control for the 120VAC heater
The only part of an RV fridge that runs on 110AC is the heating element. This element should be isolated from the chassis, something I can check the next time I'm at my RV. This isolation is necessary to prevent having 110AC appear on exposed metal parts of the rig.
My Dometic installation manual shows, where circuit diagrams are provided, that the heater is connected between the hot and neutral AC power lines. It does not show that either of the lines is connected to ground. One of the lines goes through a thermostat control to switch the heater on and off as needed. If the contacts in the thermostat become pitted, heat will be created across them which should eventually cause component overheating.
I suspect that the bad plug the RV technician found was a coincidence to the overheated control board and not its cause.