Arrods, I'm not clear where you're coming from, and what you say isn't altogether correct. If the Third Party has an excess on their policy, their own insurer will pay their claim then seek reimbursement from Hopkirk's SIL - but they won't pay the excess, the TP has to seek that themselves from Hopkirk's SIL via her own insurers. This has always been the case.
It's the total cost of the claim we're talking about here, and as we've said already, all the information is third hand via a relative - we don't even know accurately what it says in the letter.