HH confesses to pushing Sawyer down the hold. he also confesses to getting wellard in on the plot to kill sawyer while the spanish were trying to take the renown. the confessional letter (ficitonal of course concocted by the "biographer") was written later and is, in my opinion, very much out of character. HH is more a man to let his guilt fester and destroy him from within then to let it all out in a letter to his descendents.