What the above is talking about is on the client side.
To answer that, all users that can log-in (with the exception of root, see below) should not be in the local machine's /etc/passwd and /etc/shadow.
Instead, those users should be in the NIS server's /etc/passwd and /etc/shadow
- Tip use NIS+ instead of NIS.
- Tip that article was written in 2003, I might suggest a newer one :)
Why leave root in /etc/passwd and /etc/shadow?
Suppose something bad happens (NIS server goes down, network is down, config file gets messed up), if root was removed, you'd have to reboot in runlevel 1 (or whatever the systemd equiviliant is) and then get the system back up and running. When you leave root's credentials on the box, you can log in live and do repairs. There are security risks involved, but follow best practices.