Spartacus,
The fridge may be a lost battle since you signed it, but the other stuff may not be. Were the items in numbered boxes, or in a box that was on the shipping list? They can't list every single damn item that is in each box so the items don't need to be on the manifest per say. Now if you are saying that they shipped un-marked boxes you may not have any ammo to fight with. Even in that case, I'd try to fight it.
Hindsight is 20/20. I've been PCS'ing my entire life and one thing I learned was to photograph all high value items...from several angles. And then I won't let any HVIs get packed without my wife or I being there and then confirming it's on the HVI list. Very tedious, but worth it in the long run. For everything else I usually walk through each room and take a few pics while everything is still out. Saved me about $500 this last PCS when a bunch of stuff showed up covered in mold of epic proportions. All because someone spilled coffee on some of the boxes.