Although the first part of the link deals with authorizing remote control of your system, "Accessing a Remote Ubuntu Linux Desktop using Vinagre" seems to discuss the reverse, i.e. commandline to connect to the (client's) system thus:
ie the ip address of the remote system. Maybe you could experiment by working 2 laptops side by side on your home system, then try a connection to a friend's computer while on the phone to them.
I can't check this out as I have Ubuntu not Fedora. For the ubuntu/debian systems, rfb authorizes remote control, maybe sometimes krfb/grfb depending on your desktop installation, with rdc (or krdc) to connect to the remote system. I use this within my own network. If you can't get a solution within Fedora, I think a dual boot would be worthwhile, doesn't take long to install.
With any remote work (including ftp) I have found that the only problem is the syntax used to connect. I recall that when connecting to a remote computer, the syntax was (ip address or hostname/session no:5900), the first login was session no.0, and so on. I might be getting my : and / mixed.