The root password prompt pops up when trying to connect to a new WiFi network,
whether that network requires authentication (in which case it still pops-up
even if you choose to only save the password for just the current user) or not.
This makes it impossible for someone without the root password to just use any
public wifi. We should default to saving the authentication password, if any,
for the current user (by default it tries to save for all users, which is
really ugly) and then just stop asking for the root password.

There are some old related bugs, all closed: bug 751211, bug 780137.