It's still a struggle, and I thank everyone who has tried to help.
Here's what I've done so far.

I've succeeded in getting this command to work:

[bobkatz@localhost etc]$ rsync localhost.localdomain::
Backup-Data-Folder      



"Backup-Data-Folder" is the rsync task (module) named in rsyncd.conf

However, this command does not work:


[bobkatz@localhost etc]$ rsync host::
rsync: getaddrinfo: host 873: Name or service not known
rsync error: error in socket IO (code 10) at clientserver.c(125)
[Receiver=3.1.2]


AND, backuppc gui reports:


Host localhost.localdomain Backup Summary

This PC has never been backed up!!

This PC is used by root.
Last email sent to root was at 7/7 01:01, subject "Backuppc has not
backed up".
Last status is state "idle" (backup failed) as of 7/11 13:47.
Last error is "No files dumped for share Backup-Data-Folder".
Pings to localhost.localdomain have succeeded 184 consecutive times.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I have tried several UID/GID settings with no luck.
        
My current rsyncd.conf file is as follows:

#######################################################################
##
##  RSYNCD config file for the backuppc server
##
#######################################################################

gid = users

read only = false
# false will allow backuppc to restore files to the server
transfer logging = false
 lock file = /var/run/rsync.lock
 log file = /var/log/rsyncd.log
 #pid file = /var/run/rsyncd.pid
## host allow: this is important.
## In my case leaving the subnet-mask leads to a failure,
## so I only provide the IP.

 
## Now you have to declare, in brackets, the RSYNC 'module', or "share
name" as it is called within backuppc
   [Backup-Data-Folder]
   ## Next, set the path you want backed up. Be sure to use a trailing
slash
   path            = /
   read only       = no
   list            = yes
  # auth users = user1
   hosts allow = 192.168.0.217
   #secrets file = /etc/rsyncd.secrets
   ## the easiest way is to use the root user
   ## This user has "ROOT"-privileges, so he can save files.
   # uid             = root
   # gid             = nogroup


   uid             = backuppc
   gid             = root

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