I can't now get the fridge in our rig to cool down on 120v, but it does fine on gas. There is confirmed 120v to the receptacle the fridge is plugged into. A couple months ago I ran a test from the portable gen with the fridge on 120v and a Kill-a- Watt meter that showed the fridge was pulling about 350 watts. All good.
Now just plugged into its own receptacle (120v confirmed) the Kill a Watt shows no watts draw at all and no cooling is happening in the fridge. I have not found why not yet, but I expect to eventually.
Point being, these things are not very sensible in how they act, so don't spend any big money right away until you are sure what's what.