My GAP insurance is through my credit union who I have my loan through. They pick up the extra coverage that does not get paid by the insurance company. This is what their website says:
You could lose more than you might expect if your new or used vehicle is totaled or stolen (and not recovered). Since most insurance policies only cover the value of your vehicle minus any deductibles, your loan balance might be higher than your insurance payout. Now you can protect yourself with Guaranteed Asset Protection (GAP), which pays the difference between the value of your vehicle and the amount you still owe. Plus it covers up to $1000 of your insurance deductible.
Sounds like whomever you have GAP though doesn't want to pay up?