That's not quite how it works. The subreddit and UReddit.com sites are not connected like that.
Teachers go in and list their courses, syllabus, and relevant information to make it easier for folks to find after the content falls off our front page. There is also a messaging feature so that once a student enrolls (adds) a class, the teacher can message them with updates. So it is an aggregator or sorts, but it's also a tool to increase communication and organization. As far as using the term University, unfortunately that was picked in 2010, and we often just go by UReddit.
They are actually kickstarting a platform, OpenCompass that much more closely resembles Coursera/Udacity. Perhaps a minor reason for that was to help get away from the word University as they grow. Possibly Reddit too, their default homepage isn't exactly gleaning with intelligence most of the time.
(There are actual legal guidelines for using the word "University" in some states and countries; I wonder if the name will last.)