[SPOILER] ____ was a traitor?

SPOILER ALERT: Do not read if you have any plans to finish Assassin's Creed: Brotherhood and/or Revelations (and have not done so already). 

I've been playing through Assassin's Creed 3 (love it, but I'll write about the whole experience at a later date) and during one of the first sequences in the modern timeline you start talking to the other members of your party about Lucy Stillman. Particularly, one conversation with Desmond's father where Desmond talks about how he (again, SPOILER) killed Lucy at the end of Brotherhood. But what specifically surprised me was when he said that although Juno took control of him, he agreed to kill Lucy because Juno showed him what would happen were she allowed to live.

You beautiful traitor...

It's at this point that I go, "Wait, what?! Lucy was a traitor?!" But then I talk to other two and they both talk about Lucy being a traitor as if this is old news. Now, I played through Brotherhood and Revelations and at no point do I recall anyone mentioning anything about Lucy being a Templar. I found some videos showing clips from Revelations that seem to hint at Lucy being a Templar, but it's mostly people trying to support their theory (admittedly, their correct theory) that she was a traitor.

So, if nothing definitive was ever shown in the previous games, then why is the revelation (to me, at least) that Lucy was a Templar, treated like it's yesterday's news? Until I started searching around, I believed I had missed something crucial in the previous games. Did anyone else have a similar experience starting out with AC3? Or did I actually miss something crucial in the last game?

Relevant Links:
Lucy Stillman Wikia