Hey Tom Price,
Thanks for using Explorer. The search in Explorer works similar to the search in ArcGIS Online, in that you will only see items that you have access to. Since you are the admin you have access to everything in the org. If you sign in as a user who does not have access to a map, you will not be able to find the map in the browse list or search for it. The map has to be explicitly shared with the Organization or a group that you belong to.
Joel
