"There lies the rub," as a famous quote from Hamlet would put it. One of the reasons I personally find this novella so compelling is the way that Henry James presents himself as the master of ambiguity in his presentation of the account of the governess, and through the way that we are never entirely sure if she is an unreliable narrator or not. Let us just remind ourselves of the facts: the only person who ever sees the ghosts is the governess herself, who is an impressionable female sent to an isolated mansion by an attractive older man who she clearly is drawn to. Critics point out the Freudian nature of this relationship and the potential desire of the governess to create a situation that would cause her employer to visit.
Thus it is, that if we examine the powerful ending of this story and in particular the supposed confrontation that the governess and Miles have with Peter Quint, the account of the governess is cast into doubt. Having "won" Miles and triumphed over the nefarious intentions of Peter Quint, note how the governess describes the tragic ending:
With the stroke of the loss I was so proud of he uttered the cry of a creature hurled over an abyss, and the grasp with which I recovered him might have been that of catching him in his fall. I caught him, yes, I held him--it may be imagined with what a passion; but at the end of a minute I began to feel what it truly was that I held. We were alone with the quiet day, and his little heart, dispossessed, had stopped.
Focus on the strength and "passion" with which the governess "caught" Miles. It remains unclear whether Miles died because his heart stopped because of the shock of the confrontation with Peter Quint or the deranged governess suffocated him with the force of her embrace. We are never given an answer.