Steven ZahmActually it is much simpler than that.
To allow the public / non-users to view the “Public” entries, nothing needs done. The check boxes you referenced, should be unchecked.
To require users to login to view the “Public” entries the “Require registered users to login before showing the directory.” box must be checked.
The two shortcode overrides, generally, should always be un-checked. Those allow the shortcode options to override the “Require registered users to login before showing the directory.” option and allow the display of an “Public” or “Private” entry. You only really ever want to enable these if your directory is private and you want to be able to display and entry without having to open up the entire directory.
When the directory requires login, the definition of “Public” and “Private” entries changes which can be confusing. I hope that helps! Many thanks!