I'll report my experiences with Ubuntu here when I'm done.
Quick update: Latest Ubuntu distro fails the same basic test as gOS did.
I simply tried to set the time clock to update automatically from the internet. It told me a I had to install NTP support to do so. I pressed the "Install NTP support" button.
This one did slightly better than gOS did: It actually prompted me for the administrator password to install NTP support. It worked, downloaded the NTP support package, and installed it. Underneath a "DETAILS" button, I could open a little window and see the command-line shell output from the thingy that installed and started the NTP support. I could clearly see it saying "NTP started". So far so good!
After closing that window, I tried to set it to get internet time automatically, and...
"NTP Support is not installed. You must install NTP support..."
Ad infinitum.