At first we had this issue with my wife´s iphone 6 with ios 9, but not with mine. With the ios 10 update, my iphone started acting out, messing -- as described by many in this thread--, the same photo library that we update via iTunes sync.
We found a solution for both cases.
After reading this thread I deleted the "iPod Photo Cache" file on my pc and changed the iTunes sync folder to a new empty one. Synced the iphone with the idea all pics were going to be deleted and it seemed that way. However, when I checked: settings > general > information, although it showed 0 photos; on general > storage & iCloud > storage management, the photo app showed it was using 1.7 Gbytes. Meaning that somewhere the iphone photo app retained a big stash of pictures. So I went to: configuration > iCloud > photos, and changed all iCloud options to off, rebooted the iphone and when it came back online it automatically started a process that restored many folders and pictures, the ones that always messed things up. I waited for the restoration process to end and synced again the iphone with itunes so the empty folder configuration was able to overwrite the restored photos. And so it did, after this sync I went again to: settings > general > information, where it showed the device had 0 pics and in: general > storage & iCloud > storage management, the photo app showed only a 96 Mbytes usage. This confirmed that the iphone photo app had no pictures left. To be on the safe side I then again rebooted the iphone and the iTunes on the desktop, selected the picture folders I wanted to sync again, and voila, order was restored, my folders and pictures were once again the way I wanted them to be. I once again rebooted the iphone to see if the problem would come back and so far, after two days and many reboots, all is well. Hope this helps anyone.
What I think happened is that users like me that like to use the itunes sync option, sometimes get back to our libraries and overwrite old versions of the pictures with better ones, and somehow the iphone starts to backup the files it deems inconsistent. So when we reboot our devices or update --as many have complained--, the crazy restore process begins and we end up with a messed up library. I think the iTunes iphone or ipad sync process should have a better validation process, and that’s the root cause Apple has address. Meanwhile this solution worked on two different iphones one with ios 9 and the other with ios 10. Meanwhile, in the future I will be careful first to remove via iTunes any folders I want to overwrite so the iphone removes all the files and no inconsistencies occur.