It does somewhat prove though that lost Bitcoin in this type of situation is actually harder to return to its original owner than if it was fiat. There's very little ways to prove you own that Bitcoin once you've lost access to it, obviously by design.
If we assume the right owner contacts you, there are ways to prove it's their paper wallet. The wallet was funded somehow. Most people create their own wallets and fund them themselves. Check the blockchain and see what address the coins came from.
Ask the potential owner where the coins were deposited from. Then ask them to sign a message from the address that funded the wallet. Or ask them to send you a few satoshis proving they have access to that address. If it came from a friend or an exchange, prove it. Have your friend do the same. If you used an exchange, and you can no longer use that old address, there is a transaction history. Screenshots can be faked. Live video calls where you are logged in and refreshing your payments page on the legit website showing an outgoing transaction to the paper wallet address not so much.