the only way for a person to prove the event is authentic is to provide their secret key, which enables the actual decryption
proving the authorship of an encrypted message is useless except if you can decrypt it and also reveal the contents as well as the authenticity behind it
quotingsecret means only one person knows
nevent1q…xvyx
private means two or more people know
once it becomes private, it is open to betrayal
and on nostr, those who are privy to a private message can prove the authorship because they can access the event and find the signature and prove it is authentic