Yes, but Baidu Jiasule is an anti-DDOS system- If someone else comes along five minutes later and says they were wronged, you can just switch it over to the new person... There'd be nothing to gain by trying to cheat.

How do you prove who was right? You can't if the user isn't able to sign the address, in which case it just becomes a communication race condition.

You could ask the user via email to send some small, but "unique", amount of bitcoin from that same address again and then refund it after you've verified that the person emailing you is indeed owner of that bitcoin address.

Why would a user not be able to sign the address? Every wallet I'm aware of lets you prove you originated a transaction by signing against the originating address.