Despite Douglas's use of ethos to assure his listeners that the governess is reasonable and dependable, the manuscript he reads ultimately reveals her to be an unreliable narrator—or, at the very least, a narrator whose perception is called into question.
This is especially the case in Chapter 20, when the governess finally tries to point out the ghost of Miss Jessel to Mrs. Grose and is told by both Mrs. Grose and Flora that there's nobody in sight. The governess previously thought anyone would be able to see the apparitions, but now it seems possible that the ghosts are nothing but inventions of her own unstable mind.
Similarly, the ambiguous ending—in which Miles suddenly dies after the governess brings up Peter Quint—adds to the question of whether or not she's a reliable narrator. Once again, she's the only one who can see the ghost. In fact, when she makes it clear to Miles that they're not alone, Miles immediately assumes she's talking about Miss Jessel's ghost, not Peter Quint's, thus proving that he really can't see what she's seeing. But the governess corrects him, and then she yells out that Peter Quint has "lost" Miles to her:
"What does he matter now, my own?—what will he ever matter? I have you," I launched at the beast, "But he has lost you forever!"
Immediately after the governess says this, Miles is stricken and falls over, giving a little whimper as the governess catches him. He dies in her arms, and though the governess seems to think that this is somehow Peter Quint's fault, it's arguable that it's her fault—she has frightened him.
It's worth mentioning that some critics have suggested that Miles may have been expelled from his private school on the (homophobic) suspicion that he's gay. This is never made explicit in the novel—it's yet another ambiguity that makes the narrative that much more confounding and, in that way, unsettling. However, this interpretation ties in with Mrs. Grose's assertion that Peter Quint was "much too free" with Miles. Of course, this reading is subjective and open to interpretation, but it's relevant in a discussion of the narrator's reliability because it could potentially clarify the narrator's role in Miles's death. If Miles was sexually abused by Peter Quint and, on top of that, expelled from school for being gay, it's likely that he would have very complicated emotions attached to the memory of Peter Quint. When the narrator literally starts screaming about Peter Quint and implying to Miles that the ghost of his abuser is present, then, it would obviously come as a terrible shock, dredging up all sorts of unresolved trauma and (given the homophobic nature of the surrounding society) guilt. In trying to protect Miles, the narrator essentially throws him directly into a harrowing surge of trauma.
Another interpretation of the final scene, however, is that Miles dies not out of fear of Peter Quint but of the governess. There are several moments in the narrative to suggest that Miles feels stifled by the governess and that he wants to get away from her, like when she speaks to him in his bed at one point and he tells her that he wants to be left alone. It's possible, then, to argue that Miles is frightened of the governess. Therefore, when she yells out in the final scene that she "ha[s]" him now, it perhaps terrifies him. Regardless of what kills Miles, though, what matters most is that nobody but the governess ever admits to seeing the ghosts, thus calling into question her sanity.