Odd that the police did not respond since there was an injury involved. I am guessing that no one told the police there was an injury because if they had, they would have been mandated to respond ... though it might have been a while.

All she can do is take it up with the insurance company. They will decide who is at fault using their own criteria and will assign responsibility accordingly. Even when she is not at fault, she might still have to pay your deductible. If the insurance company can recover the deductible, she might be able to get it back. My wife has been tagged while stopped twice, and each time we had to pay our deductible but eventually got it back from the insurer when they were compensated. The same thing might happen here.