You're not going to do it on a Linux box for sure as the tools aren't there but you certainly can run your own stuff on iOS. You don't have to sign up for anything either - just install XCode from the app store and build stuff.
> I can start writing software on Linux for iPhone, without requiring me to have a Mac
> we'll be able to develop iPhone applications from any operating system, but first Linux
> how to develop iPhone applications on Linux
^ is what I wrote, and you suggest "just install XCode from the app store"? Not sure how that's compatible.
Regardless, I hope we end with a phone that people can actually install their own software on, regardless of what laptops/desktop computer they own.
The issue is you don't have a Mac and that's really your problem, not theirs.