Updating OS X Mavericks without entering payment information?
I think I solved it.
The reason my partner was asked for an Apple ID in her user account in the first place, was because I was signed in to the App Store with my ID under my user account. After signing out of the App Store on my account and logging back into her account, she was no longer asked to enter my password or an Apple ID altogether anymore.

I would consider this a pretty strange bug, an apparently rare but easily reproduced one at that, but perhaps this will help other people who share a Mac.