Winston sees the lives every person leads as some semblance of a lie. He knows how information is mangled in his own office, and he has a vague idea that the government is indeed building and rebuilding memories from scratch every day. (Freedom is the freedom to say that 2 + 2 = 4). He sees his relationship with Julie as the only true thing in the world, and therefore sacrosanct from lies.
This is a success of his training because he is so focused on this newfound freedom, he completely allows himself to believe that the government really allows free pockets. He really believes that "memory holes" make the thing go away. He lets himself be caught out completely by his willingness to believe that truth can still exist.