Yes. If he's been given a hire car from his insurance - he's liable to pay the car until the claim is closed (standard practice). If it was given from the other party, they'll pay the bill and you'll have no liability.
It always pays well to deal with the other insurance party directly as they'll work within their budgets for daily hire car costs, repairs, timeframe etc. Your own insurance wants to maximise their own profits with storage costs, extortionate hire car costs, etc. And if the other party refuse them - you're responsible for the bill....
I may be wrong, but doesn't this depend on how the hire car is arranged.
For example, if you pay an additional fee on your policy for a courtesy car, then your insurance will pay for the car irrespective of who is to blame. If it turns out the third party is to blame then they will claim the costs back from them.
If you haven't opted in for this extra, then most companies have an agreement with the vehicle repairers that they will provide a courtesy car, if they have one available, for the duration the damaged vehicle is with them. There is no cost for this (or there wasn't last time I used this service a few years ago).
There is also a possibility, nowadays highly probable, that if you haven't opted for a courtesy car, and the vehicle repairer hasn't one available, then your insurance company, or broker, may have put you in touch with an accident management company who will offer a hire car for the duration yours is off the road.
You accept this car at your peril. If it turns out that the third party are not at fault then you will become fully liable for all costs of the hire car, and these are not cheap, after my wife's recent accident one of these companies wanted to charge over £230/day! (This was for an automatic, AWD, Qashqai.)
Also, some of these management companies are not very good at telling you that you may have to pay, but some are OK. For example, Kindertons are one of the better ones, they will look at your statement and if they think you have a chance of winning they'll let you have a car at no cost until they establish if they are likely to get their money back (normally a week). However, if the third party is insistent that they are not a fault, and the provability is borderline, they'll take the car off you. This is pretty much what happened to us, Kindertons were going to give me a car, but it took over a week to get one due to a shortage of vehicles and me insisting on a written guarantee that I would not be paying for it.
The day the car was due to be delivered the third party insurer said they would not be accepting liability.
As the repairer didn't have any available courtesy cars we ended up without one for 6 months. Had I known it was going to take that long I'd have bought one to tide us over. As it was, I hired a car as and when I needed one, keeping the receipts to claim back if we won our case. Just over four months into this saga I managed to get someone high up in the underwriters to review the video of the accident taken from a nearby property (the contracted assessors had previously reviewed it and said it was difficult to establish who was to blame, they continued to hold this view even after I'd sent them a copy of an email from the Police stating they had recommended the third party be recommended for a driver awareness course). Anyway, the manager who reviewed the video apologised and said their assessors had made a mistake, he thought it was clearly the other drivers fault and, providing my wife was willing to go to court, they would be pursuing this claim with the third party insurers at their cost. He arranged a hire car for me that day, at their expense, which we had until the day I got my car back. Looking at the papers submitted to court, this hire car cost just shy of £1,000 for 6 weeks, but it was only a Fiat 500!
