Right. The pictures are there from a backup, but are not accessible via a web browser.
Setting up as new on the phone will not bring back the photos. Setting up as new and using the same icloud account will sync back your contacts, notes, calendars, etc. If you click on the settings icon in iOS and go to icloud, those are the things that will sync back to the phone. But not your photoroll.
Thank you! It's strange how hard it was for some users to understand what it was exactly I was asking. I wonder if there's software out there to do a custom backup or sorts. I know there's backup extraction software, but it tends to be a hassle, unorganized, and is more for recovering data from a backup.