The previous post is very good advice.
It might help if I explain a bit about the “fighting it on our behalf” aspect.
You have an insurance policy with the insurer, which is a contract between you and them. Under that policy, they agreed to pay to fix your car and provide a hire car. They did that.
Your insurers now want to recover their outlay from the party that caused the damage, let’s call him Johnny No Mirrors. That claim is covered by Johnny’s insurance.
An insurer recovering their outlay like this is called a “subrogated claim”. However, because of the way that English law works, the claim against Johnny can’t be brought in the insurer’s name, it has to name you as the Claimant (and Johnny, not his insurers, as Defendant). There is a standard clause in all insurance policies that says “If we bring a subrogated claim, you must provide reasonable assistance to us in the pursuit of that claim”. This is a term of the policy, in return for which you got your payout.
In this case, the other side are, as explained above, playing hard ball. It’s just a tactic. But your DH as policyholder does have a duty to assist his insurer in responding to the tactic. However in practical terms the insurers will sort it all out between themselves. All your DH has to do is say that he wasn’t there at the time, what his interaction was with Johnny when you discovered what had happened, and that his insurers decided what to pay for the repair. He’s not on trial or under any sort of suspicion. And, as explained above, this is very very unlikely to go to a trial anyway. Insurance companies who deal with this stuff all the time forget that it’s scary and unusual for laypeople and they need to explain better.
You should also understand that, as long as you provide the requested assistance and tell the truth, there will be zero comeback for you if the claim fails.
We had exactly the same scenario, by the way. A delivery van hit our car in our street, we weren’t even at home at the time. Our neighbour got the reg. Our insurers paid us out in full. The driver’s insurers defended the claim, we got an email asking for a written statement, I wrote a 5 line email reiterating what had happened and we never heard anything again.