Why does (Apple) Remote Desktop, with client ports correctly forwarded, report as "Offline" to administrator's machine? Administration Target

An iMac Intel Core 2 Duo:


Mac OS X 10.6.6;
ARD Client 3.4-current;


Router Configuration


WAN-side TCP &amp; UDP 22, 3283 and 5900 forwarded to the iMac.
In desperation, I DMZed the administration target.


Problem

Before DMZing my administration target (i.e., with only 22, 3283 and 5900 forwarded), the iMac is listed as "Offline" on the Remote Desktop administration screen. However, I can ssh into it from Terminal.app successfully and I can control the screen — I simply can't do any 'special' tasks (copy, install, report, restart, sleep, etc): I essentially can't do anything other than viewing/controlling (and locking) the screen.

Once the host was DMZed, my administration window lists the node as "Screen Sharing Only".

Any ideas?
Does The ARD Administrator client use a ping (ICMP_ECHO) to determine client status?

A lot of firewalls silently swallow echo requests, even of the host is up.  Therefore, you may be getting false reports about host status.