Absolutely: they'd pay out to any others involved but not to his daughter. and then possibly try to reclaim their costs, as you say. Which could be a very expensive error.
I disagree with Lord B's suggestion that she would require hire or reward cover, but yes, absolutely she requires business cover if she's using the vehicle for that purpose. She's being paid by the other party to use the car in the course of her employment.
Put it this way. If- God forbid- she...