Users cannot access term reference fields (edit or view) even if they are public. Other field types that I have tried seem to work correctly (entity reference, long text). The problem seems to persist regardless of the type of widget that I am using which makes me believe that it is problem in Field permissions.
The drupal site has an "editor" role that should have permission to edit and view two fields using term reference. One field is called "concepts" and the other "audience". The "Administrator editing the node.jpg" figure shows the browser then an administrator is editing the node. The "permissions.jpg" file shows the permissions of one of these two fields. The "Editor editing the node.jpg" file shows the editor trying to change the node. Notice that the "audience" and "concepts" fields are missing when the editor tried to edit them.
I searched for similar bugs reported and even though I saw others related with access permissions I did not see one related with term reference fields.