My guess is that your fridge is maybe bigger than previous models. Maybe a 18CU FT, four door job? While they may have upgraded the fridge, they did not upgrade the inverter. An 800W inverter sounds marginal for a new design fridge. Are you sure it is 800W? Can CC offer an upgraded inverter that will run your fridge? I wonder if that tech gave you good information. Can you get him to send you an e-mail that says, their inverter won't run your fridge?
I don't know about your particular fridge. But the residential models that I have heard of, run 12V (off the truck) while towing. And 120V AC when plugged in.