If my .NET client uses System.IO.File.Copy to copy a file from \\server1\\share1\\file1.txt to \\sever1\\share2\\file2.txt
The file contents must go through the machine performing the Copy operation. The only way around this is to run programs on the target machine(s) that perform the transfer without the client machine in the middle. such as FXP which uses FTP to transfer server to server.
However, opening up this pathway may also open a security loophole and I suspect many admins would be reluctant to allow this.