PDF loaded into iBooks will not sync back to iTunes

I accessed a PDF on the web from Safari on my iPhone 4s, then opened it in iBooks. Then I connected the iPhone to my iMac and synced with iTunes. I was expecting the new PDF to sync back to my iTunes, but that did not happen.

Am I to assume that PDF files loaded into iBooks on my iPhone or iPad will NOT sync back to iTunes?

-Thanks

This definitely appears to be a bug in iBooks 3.1. I just submitted this to Apple feedback:


When I view a PDF in Safari, then open it in iBooks, it's supposed to sync back to iTunes. It just doesn't work. From your own website:

iBooks: Viewing, syncing, saving, and printing PDFs on iPhone, iPad, and iPod touch

"When you use iBooks to open a PDF, iBooks will automatically save a copy of the PDF to your iBooks PDF shelf. These PDFs will also sync back to your iTunes Book library the next time you sync your device with iTunes."