I have written a rules article. published it, and made access level on it to public. Then i noted the ID and entered it in CB.

The link looks alright, but when a new user tries to read the article it just gets that it must be a registered user to do that.

But the article it set to public.

What am I doing wrong?

Dont know why. But when I set the access status to Public on a meny item that was referring to news items it all works.

You are correct.
This way the menu has the capability to hold content which is shown based on the status of the user.
I think similarly if the module is set for access by registered users then even if the content is for Public view it will not be seen unless you log in.