If that were the case I would assume pushing the button would turn it off, since it is just a UI thing. To save file space it would only save (I would assume) an on/off for cinematic mode, and figure out the rest based on that. This would leave no reason for why it would be stuck on. Not to mention, this would be much more widespread of an occurance if it was just the result of saving with cinematic mode on.
Now that I think about it, it likely would not even save on/off, and just assume it was off, although since I am not someone who worked on their game engine, I don't know the specifics of it...