I will PM you later but in short -
a.) The insurer must deal with her claim if the driver of the vehicle was identified regardless of whether that person was insured to drive the vehicle under their RTA obligations.
b.) Did the vehicle get away or did the police arrest the driver? If arrested, then insurer will deal. If vehicle got away and it is genuinely accepted that the driver remains unidentified then she must report the incident to the Motor Insurers Bureau and proceed under the Untraced Drivers Scheme. She cannot sue the hire company as there is no vicarious liability between the tort feasor (driver) and the hire company. In certain situations it could be genuine that the vehicle was stolen without the hirer's consent. If he lives in a flat with several other flat mates it could be that one of then has taken the keys and there would be no need to damage the vehicle, but which one was it? if the police think the hirer knows who was driving they can charge him for failing to identify the driver but the insurer would be able to decline her claim as they would not have to act as RTA or Article 75 insurer = back to the MIB.