Matt,
I do not work directly with the ArcGIS Online team; however, I believe that David's answer actually makes sense and fits with the sharing model in ArcGIS Online for all content. You can share content at the following levels: Not Shared, Group, Organization, Everyone. The final level is what enables all ArcGIS Online users to see the content. It is important to note that the 'Everyone' sharing level means that everyone with an ArcGIS Online account can see the content.
The final setting that David mentioned is to allow people to view your organization anonymously (no ArcGIS Online sign in required). If you set this option then people will be able to visit your organization page and they will be able to view content that is shared with 'Everyone' without signing into ArcGIS Online.
I am glad that updating the setting allowed you to share content with everyone (including those without ArcGIS Online accounts).
Regards,
Jared G.