The resolution? Somehow, the inetd.conf file in /etc had either become damaged or (in this case) was actually missing. Ideally, you should replace the file with a fresh copy, but this may not always be feasible (note to self -- back up inetd.conf now!).
However, it turns out that as long as a placeholder for the file exists, then the Sharing Prefs will work. So if your Sharing Prefs panel is crashing, open a terminal and check for inted.conf in /etc ('ls /etc inetd.conf'). If it's not there, then type sudo touch /etc/inetd.conf. This will create an empty inetd.conf file, and fix your Sharing Prefs crash. Sure enough, when 'Crusty' created the file, the Sharing Prefs started working again!

