The alternative would be the state going: you reported a theft, we apprehended the thieves and found your stolen goods. However we can't give them to you, they belong to someone else now. That's absurd for any good that isn't fungible. Imagine losing a family heirloom, your photo collection or a Picasso that way.
1. Alice has something valuable stolen (goods or photos or whatever, doesn't matter)
2. Bob innocently buys Alice's stuff from Criminal Craig
3. Alice gets insurance money
4. Everything gets found out and Craig goes to jail
5. Alice gets her stuff back, but has to make Bob whole out of the insurance money (and maybe pay back the difference to the insurance company?)
6. At this point, it is then on the insurance company to try to recover whatever it can from Craig
That's how I would set it up if I were king anyway.
An exchange of money for an item/product is a purchase.
It might be confiscated by the Police and/or given to the rightful owner.
If you bought a thing and have the bank-/card-statement to prove the amount, you will probably get the money back, but if it was with cash, you technically don't have proof of the amount given when purchasing.