I wouldn't assume that it's the 'fridge that drained the battery. That could be a red herring.
Have you had battery drainage / no charge problems at other times?
I have been caught out with a low battery at times, either due to warn fan belt not charging, or some other mystery overnight drain. I now carry a battery pack as an insurance against this. By the way, the starter battery doesn't have to drop a lot of voltage to be too low to turn the engine.
Going back to the 'fridge issue, switch it to 'battery' symbol when driving, and 'electric' when on EHU. In neither setting should it drain the starter battery.
Hope you get to the bottom of your problem.

1990 Autosleeper Trident. Water cooled 1.9L DG + 4 speed manual box