You've been missing a lot of the threads that have offered explanations as to why Syd fought herself. It's all but confirmed that Sydney actually wanted her memory erased (or that she willingly underwent memory erasure), for one reason or another. Speculation seems to point to the fact that she was saving Vaugn's life by not making contact with him during her two-year absence, and she couldn't live with the memories from her two years. Other speculation seems to only depart from this first theory a little bit--that it was necessary for her to erase her memory in order to save Vaughn. In other words, she knew something that was compromising Vaughn's safety. Maybe the Covenant was threatening to kill Vaughn if Syd didn't give up that piece of info. Whatever the case, the theory is that she willingly underwent memory erasure to save Vaughn.
Either way, she's fighting herself in her dream because, subconsciously, she doesn't want to remember what happened during the two years. In the dream, "Evil" Syd knows things that "Pure" Syd doesn't. One of the things she knows is why Sydney/Julia willingly wanted her memory erased. Such will be one of the subjects/topics of the next episode--Full Disclosure.
As to your theory, I think's it's wrong. Beyond the fact that Syd knew a minute detail concerning Will, she also knew about her 1st edition "Alice In Wonderland" book, given to her by her mother. In episode three where she was spying on Sark and the former Russian general in Mexico, Syd knew about an unconventional method she and Vaughn had used before, i.e. setting the decibel level of the general's earpiece to high level and blowing the feed to buy time for her to take out her enemies. Beyond even that, the dreams she was having, the messages she was finding, and the memory retrieval (dream) procedure she underwent were all deeply personal, and revealed subconcious thoughts that only the real Syd could have.
