Removing OpenID login from profile "My Logins" page cause the remove of other OpenID's. In my case: additional remove of Stack Exchange and Google, so, only LaunchPad is left.
Removing LaunchPad did not affect other OpenID's.
You didn't follow that instruction.
PS: I don't know whether we can remove logins from network profile or not. But as per FAQ you can remove it from your profile page.