I am writing this as I think it out so excuse me if my mind wanders

you firewall them not
you get a push request from them and then you connect to them and use that connection to send the file.
you do a search and a hit comes back from them with a port number, you connect to them and the file is transferred to you through that connection.
both times you made the connection so it should be ok.
problem if you are not allowed to connect to their port # for some reason or your proxy server wont let you, you cant expect everyone to change to port 80 for you.
can you use a public proxy? could you connect to a public proxy port 80 through your proxy? your client wouldn't handle it properly though.
test for it? how?
you send a push request to a firewall person he cant connect to you to send the file, no port because you are firewalled, problem. no where to connect.
you get a wireless card and have all kinds of fun while the boss is not looking. his network gets hacked because they came in through your wireless connection because you didn't yank the ethernet plug!
looks like you can only get files from a non firewall host if you are behind a firewall.

did I miss anything?