TOPIC: Private Event

I have an event category 'Outings' that has 'Members' access level
I have an event under the category 'Outings'

Whether the event is set to private or public it doesn't appear for a user that isn't logged in - which is correct
However, if I link an article to the event, I can see the registration button on the article when not logged in.
If the event is private, it tell me after clicking the registration button that it's a private event and I can't register without logging in - which is fine
But, if it's a public event, I can register (even though the access level in the category is 'members').

Is this correct, or do I maybe have some settings wrong?