User blog comment:Master Sima Yi/Assassinews 03-03-'13 — Assassin's Creed IV: Black Flag trailer and screenshots/@comment-1379990-20130303192139/@comment-1153722-20130303192910

Well, Edward, Haytham and Connor could be descended from Desmond's mom, for all we know. But even though Desmond could not be 100% sure that Connor was William's ancestor too, they wouldn't have put that dialogue in just for Desmond to be oblivious to his lineage.

At the end, all the pivots stuff is about Abstergo retrieving Desmond's body from the Grand Temple, putting it in an Animus and hacking it with pivots, and then uploading Desmond's DNA (and thus genetic memory) to the cloud. Abstergo now has all of Desmond's genetic memories. Given that that is the ending of the game, expect the story to build on from that.