At Texas Woman's University reference librarians are on call every hour the library is open. Students and staff at the desk are the first point of contact but not the last point. The types of questions they answer and their training differs. Training is emphasized. For example, they are trained on the ins and outs of the databases but they don't recommend databases.
Librarians recommend resources and explain how to conduct a database search.
When librarians are on call they are supposed to check to make sure referrals from the desk are made correctly. They periodically monitor the desk. Students who don't perform correctly are dismissed. At the University of Toledo the topic has been under discussion for ten years. MLS librarians have been reduced from two to one.