You're right, it kinda happened twice, how you didn't know the assisstant (I forget her name, was it Lucy?) was an assassin and Abstergo, who were the templar, didn't know she was one and you were helping out, albeit against your will, Abstergo who you didn't know were Templars. Also how you didn't know Almualim was originally a founder of the piece of Eden and he stabs you in the back. But in both those scenarios at least one party knows which side the other party is aligned to, Almualim knew where Altair stood, and Assisstant girl knew who Abstergo was without them knowing she was an Assassin. Maybe if da Vinci and Ezio had no idea who eachother were it would be a little different, but I doubt that da Vinci wouldn't know what was going down.