VAT/motor repair/insurance claim

One of our company cars was recently involved in an accident, for which the third party has admitted full liability.  The car has been in for repair and is now ready for collection.  However, before we can collect, the garage require payment of the input vat on the repair bill of c £400. Obviously we can reclaim that vat on our next return, which is q/e 31/03/12, but why should we be out of pocket for so long and have the administration and cost around making / processing the payment. I would have thought the repair company should deal with the third party's insurance company without our involvement - after all, we're not making a claim?  The third party is an individual and not a company therefore is this a way of the insurance company reducing their loss (we can reclaim the vat but the individual cannot)? Your thoughts on the rationale for this would be appreciated, it seems to be standard practice so I'm sure there's something I'm missing.I found this on HMRC website; is this the relevant piece of legislation to allow us to reclaim the vat.  Not sure because "We" don't have an insurance claim, the other party does..?

Thanks

Extract from HMRC http://www.hmrc.gov.uk/vat/managing/reclaiming/motoring.htm#7:"Reclaiming VAT on insurance claims

If you have an insurance claim that involves goods or services that are liable for VAT, you'll normally be invoiced directly for the VAT element if you're VAT-registered. For example, a garage that carries out repair work on your car will invoice the insurance company for the cost of the work and parts excluding VAT. They'll invoice you separately for the VAT.

You can reclaim all the VAT on this invoice so long as the car is used for business purposes to some extent. This is because the work that's been done is part of the cost of running and maintaining your vehicle.

As part of settling your claim, your insurance company might supply you with other items apart from the repair work. For example, they may replace an accessory that was stolen or damaged. In some circumstances they might give you an invoice for the VAT on the item. You can only reclaim the VAT on the replacement if you were able to reclaim the VAT on the original purchase."