Multisite privacy - password option - confusing when used with custom authentication.

Plugin: Multisite privacy (this plugin was not listed in the dropdown so I just had to pick one)

We are using shibboleth authentication - users go to the main WP login page and we have a button there that tells them to login using their university ID if they have one. If they don't have one, they can login via the local WP authentication. The password option of multisite privacy uses the main login page which tells people to login using their university ID = which of course won't work...it's confusing. Do you have any suggestions for making this clearer? We could use CSS on the login page but I don't know if that would help.