Homeowners denied my roof claim, any recourse?

In the BR area, State Farm insurance. After the severe weather a couple weeks ago, I found some shingle pieces in my yard. I know damn well we got hail both days, I sat outside and watched it on Thursday and my son said it was worse Monday (I was at work). I know a lot of wind and things hitting the house. Trees down all around the neighborhood, neighbor's tree down etc.

So I called a few companies to come out and do their free inspection. Note, my roof is pretty old, but doesn't leak and I never saw shingles like that before, even after the hurricane. They all told me there was damage, and it was worth filing a claim for insurance.

I filed, the adjuster came out, and denied the claim. Said there was no evidence of hail or wind, just wear from age. I got the rejection letter within an hour after he left. The contractor I had settled on was surprised, says I should file an appeal because there is clear damage. Says there can be some depreciation due to older stuff, but he said the adjuster just ignored what was there. Told me to send that letter to my agent along with his estimate, and appeal.
He told me he's been roofing since Katrina and hasn't seen something like this ever.

Is this a normal thing, just the game they play? I know the contractors want a check so they may play things up, but the companies all said I had serious damage and it shouldn't be a problem, the question was how much I would get.