I watched the musical in January and I just finished the audiobook version of the Chernow biography of Hamilton (pro tip: listen at 2x speed to save 19 hours) and I have to say the musical stuck VERY close to the biography. A few embellishments for dramatic effect but the substance is all spot on. Unless the biography is flawed, I'd say that ‘Hamilton’ and History are very much in sync.

In case you want to learn more, I posted "Three Timeless Truths Entrepreneurs Can Learn from Alexander Hamilton" earlier today based on what I learned from the biography: https://news.ycombinator.com/item?id=11475047