Well if we're on Twitter and I want to send you a non-public link (just between you and me) then you have to make a dropbox account. Or a Box.net account, or a Mega account, or every other kind of account you might get sent to. If we're talking on app.net, I know I can send you a file hosted there. I know twitter added inline photo support recently, but app.net had it first.
The APIs are designed for web apps to be built on. It's not really a stand-alone service, it's more like data storage & identity management for you to make web apps on top of.
You need to upload the files to some place. He's saying with app net it's possible to upload it to the network (like Twitter) itself, and not to some third party storage like dropbox/mega/box. Just like sending images on Twitter.
You have to make a dropbox account to see my file, if the file isn't public.
Edit: wait, maybe that's not true. It's even worse - anyone with the shared dropbox link will be able to get at my file even if they're not authenticated as someone I want to share with.