Wait, isn’t it possible that August put the story about Bae in at the same time he added his own story? All we know is that the picture of Bae is there at the time of S,B,&T. We don’t know it was in the book before that point. Does Henry comment on Pinnochio’s story increasing? I kind of thought he was less worried about the book, and more on getting Emma to believe at that point in time, so he might not have noticed if there were stories he hadn’t seen yet.
In any case–whether August read about Bae in the book begs one question–when did he do that? Because far as we know, he had not yet been to SB when he cornered Neal in the alley. So there has to be more story here, either August came to town on a previous trip before finding Emma, or someone else told him about Bae, or he knew him becasuse he met him. I really like the idea that he is on the run from the HO. It would lead to better in-story reasons for why August felt it so necessary to separate Neal and Emma.
“If I had a world of my own, everything would be nonsense. Nothing would be what it is, because everything would be what it isn't. And contrary wise, what is, it wouldn't be. And what it wouldn't be, it would. You see?” -- Lewis Carroll, Alice's Adventures in Wonderland & Through the Looking-Glass