It's an edge case that someone will unsubscribe from someone else's mailing list or click it by mistake, so making every single person (99% who are unsubscribing on purpose) confirm, log in, enter their address or receive a confirmation is an infuriating waste of time.
The best way to mitigate this is a simple "You unsubscribed whatever@gmail.com", with a little undo button in case it was a mistake.
And if all this still goes wrong... if the person liked your newsletter enough, they'll figure out what happened when they stop getting it.
(Side note: I've really been hoping GMail and other clients would accept a URL in email headers that would handle unsubscribe, so they could add a button to the UI. I know that's oversimplifying everything, but it would significantly improve the email experience.)