Auto Insurance Claims: Auto claim, repair estimates, collision report

Question
My car was rear ended. Even though it's a small dent, but I want to fix it. I have been keeping this car in an immaculate condition and I don't want the dent to look at me every time I'm looking at it. The mistake on my part is that I received a phone call from the opposite party's insurance company that stated the repair price between my body shop and the opposite party's insurance company has reached an agreement. I took the phone call as a go to proceed with the body shop appointment and took my car in. This is my first auto claim so made stupid mistake of not waiting for the check arrival before starting the repair work. I have all the documents that proof the opposite party is at fault and had file a collision report because the city police is not responding to non injury accident anymore.

Two days had past and my body shop called and said they haven't received the check and found out the liability claim has not been approved yet. I haven't got hold of the adjuster that works on my claim. Should I worry about the opposite party's insurance company will reject my claim? If the claim is being rejected, how should I fight for this claim? Opposite party's audit department already negotiated a lower repair cost than the original estimate cost. All I'm asking is to fix the dent and not asking for the lost of my car value. I don't want to incur legal fee on my part if this is not a winning case. What is your opinion on this?

Answer
I don't think you have anything to worry about.  Repair estimates are just that - estimates.  Different appraisers will rarely write the same estimate.  Also, body shops are notorious for over-writing estimates because they earn more that way.  Insurers write their own estimates to prevent body shops from over charging.  Body shops almost always accept the insurer's estimate and work off it.  It usually has a lower hourly rate and the shops accept it because they know it is fair.

If the insurer agreed to cover your repairs, they will likely do so.  Just call the insurer and get some clarification.  If your claim rep is unavailable, ask to speak to another person.