There really are no Michigan cases that hold that the repair work actually has to be done in order to collect the $500 mini-tort amount. All you have to do is prove that damage exceeds $500 and that the other person was at fault. This doesn’t mean that a particular insurance company or Judge will have the same opinion. What you should do is tell the insurance company that if they don’t pay the $500 based on the reasonable proof you have provided, that you will sue their insured (in Small Claims Court). If they do not pay, then proceed with your lawsuit. If the driver and car owner are not the same, sue both.
Steve Gursten's answer above is 100% correct. No surprise given his stature as a leading authority on Michigan auto law. Following up on his answer, get a few estimates from body shops to present to the insurance company. If they still deny, file your suit but be prepared to have the estimators come to court or get a certificate that indicates the estimate is a business record prepared and kept in the ordinary course of their business. This is a another example of an unreasonable insurer, and why this State so badly needs bad faith insurance laws to punish these greedy insurers who deny meritorious claims.
Of course, this is not meant as legal advice nor does it establish any professional relationship.