If you click on active topics, the last posts of all members only sections are visible, even when logged out.
As are all the members only forums in the Forum List.
That is either a bug in the script (forum software) or an error in the setup, or both.
If it is possible it would be best to make the "Active Topics" menu item visible (or clickable) only to members. It is probably possible in the same way that "Search" is only visible if you are logged on.