If they were trying to pull a fast one, they'd tell you the entire wiring in the car shorted out and caught fire, leaving you with a bill for all new electrical wiring, and installation, which they could've easily told you. Compared to that job, a fuse box is nothing in regards to price. Is OP a mechanic by trade? Is her father? You said she skipped a fuse box, or a few fuses... correct? What diagram are you even looking at that's outdated?
It's very likely that there was in fact no melting visible from the front. Did she remove the fuse panel to inspect it completely? It's entirely possible that they're telling the truth, but hell, get a second opinion from an independent mechanic or another dealership if it'll make you sleep better. It'll cost you more in the long run to do so, but hell, you don't want to be screwed over right? It's worth it to pay a couple more diagnostic fees.