@Willa: tkavan is talking about kepubs purchased from the Kobo shop. Information about these are kept on the server and synced between the device and the server. If you have multiple devices, or use the app on an Android or iOS device, this can also be synced.
As the reported problem, I have noticed something like this, but with respect to the multiple devices. Finishing a book on one device, syncing that device and then the other doesn't mark the book as finished on the second device. But, it will transfer the reading position between them.
I think this has changed with recent firmware, but I only had one device last year and didn't read many kepubs. I think it is restoring the last non-finished reading position that was saved, but I am not sure.