As I understand it the Mongols didn't write much down during Genghis's early life and most of the people around him at that point would probably have reason to exaggerate or play along with whatever story they wanted to go with. I only thought of this because of his relationship with jamukha and how unlikely it seems he really met him at a young age, teamed up with him later as they both walked different paths to positions of power, and then became mortal enemies. Idk it just seems too story book to believe and it got me questioning who this story came from.
Christopher Atwood, a historian and linguist of East Asian culture and also the man who compiled the Encyclopedia of Mongolia and the Mongol Empire says this:
The details of Temujiin's rise to chief of the Mongol tribe are told in the Secret History of the Mongols, the Shengwu Qinzheng Lu, and Rashid ud-Din's Compendium of Chronicles. While often sharing episodes, they also diverge on many points, particularly chronology, and it is difficult, if not impossible, to reconstruct a synoptic narrative of his political vicissitudes before 1201.
Let's start with the Persian chronicler, Rashid al-Din. Though he is an important source for history in general (not just the Mongols), it is important to note that his information came later. He basically drew upon the SWQLZ (Shengwu Qinzheng Lu) and the Yuanshi, and then added much of his commentary on top of it. Another important note is that his understanding of the geography beyond the Middle East was not the greatest.
There are other sources that talk about the early life of Genghis Khan but many of those sources came later, so these 3 are generally the ones cited even in those later sources. Many historians have considered the SWQLZ to be the most comprehensive early source because it's more structured than the Secret History is; BUT, the problem with this particular source is that it does get some things wrong once the Mongols break out into China; two examples being the dates of various raids or the Siege of Kaifeng.
Finally we have the Secret History of the Mongols, which is an incredibly important document in history. The main reason for this is because the history of the steppe peoples is shrouded in mystery and we've always relied on outside sources only. The Secret History was a history of steppe peoples from steppe peoples. Regardless of this, I will say you are spot on when you say it seems too "story book." The Secret History most definitely at times seem to be written in a style of an epic and sometimes even a drama. Perhaps it was meant to be that way to add some tension and some legend to it, but it is not all like that and the author does say some negative things about Genghis Khan.