By specifically testing it. I even made an extra account to get a clean state. You can check its memory interface and find nothing, delete all chats. It will still remember it. If you delete that and start a new thread, it may even mention the fact then say it forgot it at the user's request.

You can't tell me "that's not true". If my account's memory is empty and I've deleted all chats and it still remembers things there is some hidden form of memory. It may be intentional. It may not. But it's retaining information in a way that users can't manage.