Firstly, the Knock for Knock agreement between insurers was stopped the best part of 20 years ago.
Secondly, it is a basic tenet of insurance law that anybody having a claim must do all to mitigate the loss - in other words to act as a prudent uninsured (so the question that one needs to ask oneself is if I was uninsured, would I hire a basic car or would I hire a like for like car?).
Thirdly, if your policy provides a courtesy car whilst yours is undergoing repair, it is likely, as has proven to be the case in your situation, that your policy will provide you with a car to keep you mobile - the car will, in all likelihood, actually be owned by the garage doing the repair as your insurance company will have a contractual agreement with the garage for the provision of a basic courtesy car.
Fourthly, and this is where it gets messy and flies in the face of the mitigation requirement, if you are contacted by a credit hire company, they will hire you a car of your choosing, you sign a rental agreement, and then they pursue the third party insurance company. If they are unsuccessful, you will be required to pay for the rental.
One of the many reasons why car insurance premiums are increasing is because of credit hire companies (a few years ago my brother in law was shunted in the back of his 5 year old Audi A4 Estate - he was provided with a brand new BMW X5 for a month by the credit hire company - I dread to think how much this cost).