I wouldn't give up either. If they can show that the damage was caused due to stone impact to the radiator then my argument would be as above i.e. the design is wrong and a radiator should not get punctured by a stone. However even if it did puncture it the light should have come on to warn you to stop the car. It will be a struggle but I know that I would eventually get them to admit it.

 

If the radiator is holed and the car looses water the warning system should tell you before serious damage is done. The practicalities of that are irrelevant and not your concern. I'd take the advice above and fight on....good luck.