I'm no rsync genius, but using the scp like syntax I can't seem to get it to
copy from remote server to remote server. 

I'm using:
rsync  version 2.6.1  protocol version 28
Copyright (C) 1996-2004 by Andrew Tridgell and others
<http://rsync.samba.org/>
Capabilities: 64-bit files, socketpairs, hard links, acls, symlinks, batchfiles,
              no IPv6, 64-bit system inums, 64-bit internal inums

rsync comes with ABSOLUTELY NO WARRANTY.  This is free software, and you
are welcome to redistribute it under certain conditions.  See the GNU
General Public Licence for details.

The command and results:
root@rocket sbh # /usr/bin/rsync -av --progress --one-file-system --stats
root@tulip:/home/trish/ root@shapeshifter:/mnt/aux/tulip
Warning: No xauth data; using fake authentication data for X11 forwarding.
receiving file list ... 
17330 files to consider
mkdir "/home/sbh/root@shapeshifter:/mnt/aux/tulip" failed: No such file or directory
rsync error: error in file IO (code 11) at main.c(346)

Now, I double-checked on shapeshifter and /mnt/aux/tulip exists, I'm not really
sure why it's putting that directory name in the front of it, or how to stop
that from happening, but at this point in time it looks like a rsync bug to me.