There might not be any anonymity,  but that still doesn't help you prove that a specified person owns the private key associated with a newly generated Bitcoin address,  whose only transaction so far was to receive some coins.

Unless the person shows you the private/public key; for all you know,  the Bitcoin address was a DUMMY address, and the coins are essentially destroyed --- since there is no known public/private key pair in existence  that would have the address that the coins were transferred to.