When I transfer files between servers on my desktop is my computer an intermediary?

If you are using Windows Explorer on desktop A to transfer files from server B to server C, then yes the files are traveling from B to A to C.

The easiest way to bypass this method is to use a Remote Desktop Connection to server B and then copy to Server C.

There are other alternative methods, such as using telnet, ssh, scripts, and 3rd party programs that allow you to bypass the middleman.

The answer is yes, the files are going via your desktop when transferring between 2 remote machines using explorer. You can always remote to one of the servers and move them directly from one to the other.

If both have FTP servers running, you can skip your desktop from the route using Flash FXP. It does exactly that. IF not enabled by default, it takes 2 clicks to enable the FXP mode on most FTP servers.

FTP is designed to take care of file transfers (File Transfert Protocol). Much more reliable & efficient than native OS copy / move.