Then the fault must be in the fridge. Probably just a chafed or squished wire. Ever had the cover off?
I bet it would if you put a 20 amp fuse in the fridge ;)
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I had an interesting problem a few years back with my engel. The socket for the 240v lead broke so I made up a 3 core flex lead attached to the rear of the broken 240v socket and connected a 3 pin plug. What happned next was fun. I f I ran the engel on 12v I found I could connect a 240v bulb or fluro light to the 3 pin plug and it would light. The fridge was generating 240v and was back feeding to the 240v input. Great emergency light.
As Utemad says, you have solved half of the problem - the earth, but where is the power coming from to make the fridge live at the handle.
You say it ran okay inside the house and wasn't live, right ? Silly question but how did you and the multimeter (wonders never cease:D ) test to see if it was live or not.
Do you use the same cable for the car as you do in the house via an adaptor ?
If not then me still thinks the cable you use in the car is faulty.