Beav.es is a custom tool that has been developed on top of the OSU Drupal distribution. It uses a contributed module called shur.ly, which provides the base functionality for the URL shortening service.
Due to how the shur.ly module is built, to allow users the ability to create custom URL paths would require providing a permission that would allow them to both create and edit all paths in the system, even ones that aren't their own. This would present a security issue.