The light inside the fridge.. The "power wire from the switch" may well be a ground.. Just so you know.. I think on mine the switch is on the ground side of the socket.
Shoot me a photo of the switch and lamp and I may be able to tell you more than you want to know.
But.... It matters not which side of the lamp the switch is on
The switch on mine is two spring copper leaves. The lever seperates them when pressed, when the lever is released (by the door opening) the leaves touch.. Unless someone ran a screw where there should be no screw this may be where your problem lies.
HOWEVER there is an even EASIER explanation,
Some DOMETIC models have a switch I think it's labeled LAT and it is normally above the door, You may also have a Humidity control switch there.. The LAT switch.
Turns on the light even if the door is closed.
Yup, that's your problem LAT switch is on.
What is LAT... Low Ambient Temp.
Seems that if it's too cold the Fridge does not work well so they turn on the light to warm it up a bit.
Home is where I park it!