Unfortunately could not confirm your issue. Please see the below image representing it's functional.



Please ensure your Joomla content categories and articles themselves have appropriate access (set to "Public" for testing).

Please PM backend login credentials. Please also provide a URL in the PM to a users profile that is NOT showing articles publicly. In the above test I was not logged in while viewing a users profile and articles displayed fine; issue appears specific to your install (likely configuration based).

Have reviewed your instllation and they are not displaying to public users because you destroyed Joomlas usergroups designed. This will cause massive adverse affects throughout CB, Joomla, and other extensions.

Not Valid
Public
|— Registered
|—|— Moderator
|—|—|— System Admins

There was absolutely no reason to perform the above and could've been left exactly the way it came. Deleting the other CORE usergroups is where the problem begins. The system is having too difficult of a time determining who is a public user and who isn't. I've no idea how to restore this except the direct query below.

With the above it will first purge the usergroups table and restore it to J1.7 fresh install defaults. You may need to change the jos_ prefix if this is not your DB table prefix. The 2 example groups Joomla provides are safe to delete. The defaults however are not (don't understand why Joomla lets you delete them to begin with). This will result in the below.

Valid
Public
|— Manager
|—|— Administrator
|— Registered
|—|— Author
|—|—|— Editor
|—|—|—|— Publisher
|—|—|— Shop Suppliers (Example)
|—|— Customer Group (Example)
|— Super Users

It's very important for the defaults to keep their respective IDs as CB uses them to map users appropriately. By deleting, re-creating, etc.. through the GUI they are given a new ID which will no longer allow CB to properly match against and will fall back to very basic parent>child relationship permissions.