Comment 1 for bug 2022825

The /etc/default/motd-news file is read by the /etc/update-motd.d/50-motd-news script which is launched by motd-news.service. It is normal that setting the option in this file will not stop motd-news.service from running - however, it makes the script a no-op that does not access the network.

Are you seeing the motd-news.service access the network and make changes to files when ENABLED=0 is set? This is what is guaranteed by https://ubuntu.com/legal/motd.

You are free to disable the timer service as well if that is your preference. The documentation tells users how to disable the service without having to know systemd service interfaces.