I don't know about any of this stuff saying you need to run your fridge once a month, but I've not done that on my 2003 TT with a Dometic fridge EVER..
I'm only a "fair weather" camper, so my TT sits more than it's in use and when it's stored for winter, it's off from the end of Sept to sometime in May.. It has always cooled down and I shut it down between camping trips between May and Sept..
Do what you think is best, but I've never heard of that and my fridge keeps my beer cold every summer, so there you go! :)
Mitch