Under Michigan law, if you are 50% or more
at-fault in an accident, you can be sued for
up to $500 in damages to another person's
car which are not covered by collision
insurance. Most companies offer this
coverage, which is sometimes called minitort
coverage.
But this doesn't deal with your situation where their insured was at fault. I think they are trying to snow you because this has nothing to do with no-fault.
It does not list Collision as one of the benefits discussed that fall under no-fault.
So I would go back to her insurance company and ask to speak to a supervisor. Explain that you weren't hurt in the accident, nor do you intend to sue. All you want is for your car to be repaired. Since their insured was 100% at fault, you are expecting them to pay for those repairs.
If they still refuse, you will have to sue them.