Hm, that doesn't seem to have been it. When I go into the "Authorize this computer" screen it says that I have already authorized this computer. (So in theory it should all be fine. So what the fuck?)

So it's not that it thinks I'm on a new computer. That's not the problem.

Perhaps iTunes is poor with regard to its handling of differing user accounts. Perhaps they've only accounted for the condition of a reformatted computer, not a changed user account. They don't seem to understand that you can have more than one user account on the same computer.

In the meantime, I'm working around it by using CopyTrans Manager to manage the songs on my iPhone and to transfer songs to it manually. iTunes is now relegated to being an outlook-contacts-synchronizer only.