In NY, I was rear-ended pretty badly by some teenager who was texting on her phone. It was stop and go traffic.
The claims adjuster came to my house to look at the damage. As with you, he said he can't tell the damage because he can only see the visible damage. He then wrote me a check for what he saw. I'm driving a bmw and I said there's no way the damage is for $1,800 only. It's at least a $5,000 job. So, the next thing I had to do was find a shop. I went to my dealer's shop as I wanted a certified BMW specialist to work on it. The shop then worked with the claims adjuster to write an additional two checks, totally over $5,600 to complete all the work on my car.
Basically, the shop told them (at a reasonable labor rate) what else needed repairing and they kept coming out to view it and write more checks. I think you need to get it into a shop that is dilligent in making sure you have fine workmanship and willing to work with the claims adjuster. My car looked completely brand new after it. They replaced the trunk, a side fender, the bumper, rear license plate bracket even. The trunk locking mechanism was also replaced. Essentially, the most important part in the process was the shop that meticulously went over my vehicle to ensure nothing was missing.
edit: I should mention in the whole process, my OWN insurance did nothing for me, as they are not liable. Talking to them just allows them to record that an incident occured. Whether they charge you more premium next period, I am not sure. Mine didn't. I worked solely with the insurane company of the person who hit me from behind. They kept reassuring me everything will be covered and to just get my car into the shop.
Also, my accident was backed by a police report. The person admitted complete fault by the way, because that's what they were at. I am sure they are just glad I required no medical assistance.