Q: I synced my iPhone and uploaded my previous purchases, but iTunes did not upload my Harry Potter books.  How can I back up purchases that iPhone didn't automatically back up?

Hi Louise8905!

I believe there are a couple of statements in the article you have linked that will answer your questions. I will highlight them here:

Can I copy my books on to other computers or devices?

With Automatic Downloads enabled, you can automatically download new purchases to your other computers or devices. Learn more about Automatic Downloads in this article.

Can I back up the books I purchased?

Yes, any books you've downloaded from the iBooks Store will be automatically added to your iTunes library the next time you sync your device with your computer. To do this, your computer must be authorized with the same account that was used to download the books from the iBooks Store.

These are both taken from the following article:

iBooks: Frequently Asked Questions (FAQ) about iBooks and the iBooks Store

http://support.apple.com/kb/HT4059

I hope that helps answer your questions. Thanks for using the Apple Support Communities!

Cheers,

Braden