Read the fine print in your insurance policy and see what is and what is not covered. If you find that you should be covered by this policy, then by all means contact the Insurance Commissioner in your state capital and report this to them. They will investigate and get your insurance carrier to cover the repairs. Happens all the time. Once the matter goes to the State Insurance Comissioner's Office magically the insurance company ends up paying the claim. Try it, you have nothing to lose.
You need to look into a reputable insurance carrier for your home and ditch the AAA carrier. Some "offbrand" insurance companies are cheaper, but they deny the claims a lot. Same goes with auto insurance, the cheaper the premium, the less likely claims are paid out. Home owner insurance is no different. I work at a "brand name" insurance agent's office and I talk to a lot of people every day and find they are unhappy dealing with the "offbrand" companies as they were denied claims for legit repairs after storm damage, etc.
Basically you get what you pay for in insurance on your home or your car.