Engine skids very commonly rust out in your neck of the woods. That sheet metal is not zinc coated prior to paint like frame members are and is quite thin.

10 years on salted roads is a decent run. I'm Surprised they offered to compensate you at all.

I would replace it and move on. You should be able to do it yourself if you are concerned about dealer labor costs. It's just a few bolts.

You might even be able to find someone giving one away since many here remove them and install aftermarket skids. I advertised a free set of factory skids just a couple weeks ago, but I live in Nevada and was looking for someone to pick up local. They went to a scrap yard.