So it looks as if your insurer's basis of settling claims is;
- in the case of repairable damage; they pay to have a policyholder's car repaired
- in the cases of a total loss; they pay cash to a policyholder to replace the car (or an item).
The second item (paying cash) would come into play where a car is damaged beyond economic repair and is written off, or stolen and not recovered, so the insurer makes a full cash settlement for the car, based on the market value of that car just before it was written off / stolen. Paying cash to replace an item; I'd interpret as paying for things such as a car stereo that has been stolen from a car. The term 'an item' is quite vague though, but IMO doesn't apply to your circumstances; your car has sustained damage as a result of an accident and needs repairing to return it to it's pre-accident state. Their policy states that they will pay to have your car repaired, not pay you cash for you to arrange for repairs independently.
The reference to policyholders making a contribution to repair costs on wear and tear items where there is evidence of wear isn't unusual. Insurers may ask for a contribution to repair costs if a repair results in 'betterment' (e.g. a rusty wing full of holes being replaced with a brand new one).
It's interesting that your insurer has said they will pay to have your car repaired at a different repairer; one that isn't part of their approved repairer network. Will this be a specific repairer that they decide upon or can it be a repairer of your choice? (I assume they would choose the repairer). That's really strange, as they will have agreed specific discounted rates on parts costs, paint cost and labour rates with their approved repairers. They'll almost certainly not have an agreement on reduced / discounted repair rates with a repairer outside their approved repairer network, so this suggests repairing your car outside their network could cost them more than if it was repaired by one of their approved repairers, unless they intend using a repairer who would carry out repairs with used/salvaged parts. I'd be looking for a pretty good explanation from their engineer on why they'll pay for repairs by a repairer outside their approved repairer network but not within their network.
I hope this all works out OK for you. Situations like this can be quite stressful. Good luck and please keep us updated!