Can they legally insist on this if the product is faulty?
In the UK, consumer law states that the seller is responsible for replacement of a faulty item or reimbursement of the cost of it (the customer's choice, not the sellers) and the onus is on the seller to prove that the item wasn't bought from him. rather than on the buyer to prove he did buy it from the seller. Consequently no proof of purchase is strictly necessary because the seller's rules can't over-rule the buyer's legal rights. An eminently sensible arrangement
It might be worth "bearding the seller in his den" and taking the stone back. A bit of polite insistence and refusal to go away often works. (Particularly if the shop is very busy at the time
)