Chapter 12, Monitoring Zimbra Servers in the Zimbra Administrators Guide [Zimbra NE Admin Guide.pdf] could use an additional note about how to enable remote collection using syslog under Ubuntu/Debian.
Instead of editing /etc/sysconfig/syslog, you need to edit /etc/default/syslogd
There's only one line which has SYSLOGD_options="".
Changing that to:
SYSLOGD_options=-r -m 0
and you'll be all set. I didn't know who to direct this to, so I just posted it here hoping someone else might get some use out of it.