How Do Extended Warranties Work?

Need some advise here. Our tow vehicle (Ford) went into "limp" mode yesterday and we wound up at a Ford dealership for diagnosis and repair. Turns out the high-pressure fuel pump is at fault, requiring a "cab off" replacement. I showed my extended warranty to the service manager who called the insurance company (CornerStone United). They told him my contract covers NONE of the repair cost - estimated at $3,500. I gave him the go-ahead to do the fix, but want to challenge the refusal of coverage. I have read the contract in detail and see no clause that would negate coverage of this repair. What would you do, to challenge this decision? I have the phone number of the insurance folks, but I'm wondering if I should first contract the dealer who sold me the contract first? My suspicion is that the insurance folks are just playing the game, hoping I won't pay attention to the details? Any advise based on your experience or knowledge would be greatly appreciated!