Under-insured car repair at a collision center

My car was hit a couple weeks ago. I had originally filed a claim with my insurance (State Farm) but was advised by my claim agent to go through the other party (Progressive) for the repair because the other driver was deemed at fault. I had taken my car to the Progressive authorized collision center and got an estimate. Progressive said that the other driver did not have enough coverage to cover the repair and I would have to file a claim with my own insurance to get it fixed. The collision center that the car is at is not a “partner” center for State Farm. My issue is that State Farm called the collision center my car is at and they have already taken apart my car. They said to get it towed to a State Farm collision center they would need to collect a couple hours labor charge for the work they did. I never authorized the teardown and the State Farm agent said that they usually do not start taking apart vehicles until they verify there is enough coverage to pay for the repair. Progressive states there is not enough coverage to cover the labor charge. Is this normal practice for them to take apart before verifying coverage? I was told by State Farm that because where it is at is not a partner I could be on the hook for out of pocket costs if there is overages