@justinlo Generally the mitigation company will come out to assist and have a contract with the customer. They may send the bill to insurance, and insurance may send payment to them directly if your contract allows it, but your contract with them if there is a direction of payment, will likely say that you will pay for whatever insurance doesn't cover. Definitely worth reading your contract.
If you had a policy limit for example, or work that the policy doesn't cover, you would owe for that out of pocket. If there isn't a limit and no coverage issues, they typically collect the full amount of the invoice from insurance and your deductible will apply to your rebuild, though sometimes insurance leaves it off the payment and then you would have to pay for it yourself.
If the insurance company called them out for you, it's likely that they are a preferred vendor and offer discounts on the equipment rental to them (PSP vendor program) You weren't obligated to use them and that doesn't mean they were hired by them.
You need to call the mitigation company and ask them if there was anything in the billing that insurance wasn't paying for, and if insurance said why they weren't paying for it. You can also ask them why it was necessary.
You then need to ask the adjuster why they weren't paying for it, if it's excluded from your policy or if you hit your limits, or if they withheld your deductible. If it's none of those things, let them know that you have a bill for things insurance didn't pay for and that the contractor is filing a lein, you can also let them know if you will need to pay for interest for late payments.
Also ask your public adjuster. If it's work that was part of the loss and not excluded by the policy, your PA should be able to help you get insurance to pay the contractor the rest of the bill. You can also ask the PA if insurance will reimburse you as cost incurred if you pay it, and if insurance will pay you any of your interest charges if you can't pay everything at once.
If there is work that insurance for some reason isn't covering but you, the PA and the contractor all say that it was necessary, a fave question is "show me in my policy where it says that you don't owe for that."
If there is work that you, and the adjusters think was billed incorrectly, or for work that wasn't actually done, then it's worth a call to the contractor to review the billing. If there's a problem with getting it corrected it's worth a google review outlining the issues with the incorrect or improper billing.
If both sides have good points or firmly believe their stances, and the PA believes it's worth pursuing you could ask about appraisal for the remainder.
Full disclosure, I work with state farm customers often, for a mit company that sometimes does PSP work. I write the bills and gather the paperwork for having state farm pay and sometimes the payments come straight to us and sometimes to the customer and we collect from them. But the customer is always who owes the money, even if state farm sends it to us for them, we work for the customer, not the insurance.
I have had claims where there were items insurance didn't want to pay for. Sometimes it's because I made a mistake, but mostly it's because they needed a little more information on what was being billed and why before they would pay. Sometimes they don't want to pay for things that other contractors don't do or bill for, though that's often just because the other contractors aren't good at their jobs or know how to bill for it.
It doesn't mean that it shouldnt be billed for or shouldnt be done, though sometimes it does mean that.
Ask some questions, see what answers you get, it may absolutely be reasonable that the contractor wasn't fully paid and you owe them money. It may be reasonable that the insurance needs to pay for some of it if they didn't release enough. It may be that you have a 10k deductible and just didn't realise that is what the bill is for.
If whatever the answer is seems unreasonable or you want a second opinion, I'm happy to look at it for you. I'm not an insurance expert and can't speak to policy but I sure can look at the mit and see if it helps!