The revelation really has nothing to do with her being a D. It has to do with the fact that of 20 Kings, one of them was a D. that was initially meant to be accepted into the modern WG.
The weirder thing is the fact that Im, the natural enemy of D., did not destroy Vivi's picture, but did to Luffy and Teach.
Theres a deeper idea here, because does that imply Lili and her family betrayed the AK? Is Joyboy even a D. Clan member?