I am not sure about the permits, but I believe they trickled in for the last fire.
the insurance company does not comp the house out they “adjust it” using a pet hired contractor who use software. The Homeowner can wait for the insurance companies offer and let their contractor repair the house or they can argue the numbers indepentdently or hirer an adjuster to scope out and estimate the loss. If an agreement can’t be reached they go to a neutral third party called a referee in an arbitration process called “appraisal” and the referee makes the decision. This is all under state law.
The terms of the policy absolutely affect the results. In the last fires the insurance commissioner and the courts took the side of the under insured and blamed the coverage deficiency on insurance on the agent. I know several companies under insure to keep rates competitive and deal with it on a case by case basis in big losses. They usually have pretty high extended coverage by implementing a rider into the contract but the insured could likely end up fighting like crazy to get into the extended coverage area.