We got hit in my wifes car many years ago and the driver, (another woman), admitted liability at the scene of the accident, but later said we hit her. We were on an island BTW and she pulled out without seeing us. The insurance companies got involved and started to fight it out even though I thought it was pretty clear cut. No expensive hire cars involved either. Luckily I had a witness and provided a statement myself from him, otherwise they were talking about a knock for knock situation.
I would check Sarnie, otherwise you could be up for a BIG bill..
Insurance companies always try and wriggle out of any costs they can. I also though that most will only provide hire cars as a short term measure, i.e. once the repairs are authorised the repairing garage should provide the car FOC or as a part of the repair cost.