How could he not have an email address with an internet connection (unless he's using an internet cafe)?
Anyway, yes one of the file sharing services should work (unless you have to supply an email address to use it).
You will need a script of some sort to allow the upload if you don't want to use FTP. I would start with hotscripts.com with my search for a script. One thing to keep in mind when adding upload scripts. You are responsible for the content on your site. Letting people annonymously upload files is never a good idea.
Why don't you just have them email the file to you? Have them change the extension to .do_ or something.
I have seen the issue of email not downloading and it's not limited to Outlook as much as it is to what firewall software you are using on your computer.
We are on Road Runner and use CA's firewall and sometimes it will not download email unless the firewall has been turned off. I have not found any rhyme or reason to it.
TCH servers run Linux and Exchange is a Windows email solution. But you should be able to add an IMAP account to your iPhone and get "push" email.
I have a Palm Treo and use ChatterEmail with IMAP and it works quite well.