Years ago I bought an older trailer like this.
All the outlets were 2-wire. Fortunately, all the runs back to the fuse box were fairly short. Back in the days when it was built it was assumed that all the neutrals would be connected to a ground bus in the box.
So we made sure they were bonded and attached to a utility company-provided ground rod.
We had to replace all the receptacles with 3-prong outlets. I stopped short of tying the ground to the neutral at the outlet, which meant that the ground leads ended up floating.
I understand PG&E's position, since they deal with the code as it exists today.
So you have the option of adding a ground lead for the particular outlet they will inspect and call it a day. Or, perhaps you want to provide grounds all around the unit.
I live in PG&E territory and find they are very safety-oriented. If their focus is just on that one fridge then adding a ground wire might be worth the effort.
Ground wires do not need to be insulated or run in conduit, but definitely run it all the way to an approved ground bus or rod.
Never rely on the structure itself to be grounded properly. It is sitting on rubber wheels, remember, and even if it is grounded at the box it would provide a much higher resistance path to ground than a run of copper wire can. Just think of how many structural panels are screwed together between the box and your outlet. Each one rusts over time. You get the picture.
Of all appliances I have owned, the one most prone to having a hot case seems to be refrigerators. So whether you get it from them or buy one on your own, you really should have a grounded outlet for it.