OpenID auth in app?

We can't do OpenID with the WGU systems as they currently stand, but this may be possible at some point in the future.  You're concerns about providing credentials to any random app are well founded.  PocketWGU requires these credentials as it currently the only way for it to connect you with the WGU servers.  You should know that the app does not communicate with this site in any way, and your wgu credentials are only ever sent to WGU servers.  In fact, your password is only ever sent to a single WGU server, and is never accessed for any other purpose.  
Of course, there's no need to take our word for any of this.  Feel free to discuss the app with your mentor or other students, you should find that it has a good reputation.  If you have access to the IT Community forum within WGU, a search will probably still show you the message threads leading to its creation, with many questions and answers regarding security.  Also, consider that WGU could easily have shut the app down at any point of the past two years.  Finally, if you have access to a sniffer (or the excellent and free WireShark program) you can monitor the traffic yourself.