The Turn of the Screw: the governess is very odd

“It was striking of the children, at all events, to kiss me inveterately with a kind of wild irrelevance and never to fail—one or the other—of the precious question that had helped us through many a peril. “When do you think he will come? Don’t you think we ought to write?”—there was nothing like that inquiry, we found by experience, for carrying off an awkwardness. “He” of course was their uncle in Harley Street; and we lived in much profusion of theory that he might at any moment arrive to mingle in our circle. It was impossible to have given less encouragement than he had done to such a doctrine, but if we had not had the doctrine to fall back upon we should have deprived each other of some of our finest exhibitions. He never wrote to them—that may have been selfish, but it was a part of the flattery of his trust of me; for the way in which a man pays his highest tribute to a woman is apt to be but by the more festal celebration of one of the sacred laws of his comfort; and I held that I carried out the spirit of the pledge given not to appeal to him when I let my charges understand that their own letters were but charming literary exercises. They were too beautiful to be posted; I kept them myself; I have them all to this hour. This was a rule indeed which only added to the satiric effect of my being plied with the supposition that he might at any moment be among us.” (Ch.13) 

(emphasis mine) 
The governess’s protectiveness strikes me as rather odd—is it pride? Inexperience? Compliance with the employer’s rule? That she keeps everything to herself and doesn’t ask him for advice is 1 thing; she even keeps the children’s letters. To me, that is odd. 
Now, what can I possibly write about The Turn of the Screw that hasn’t been written before? I won’t try to decode it. 
Let’s talk about something else. 
Look at what the governess says to Mrs Grose:

““…The more I’ve watched and waited the more I’ve felt that if there were nothing else to make it sure it would be made so by the systematic silence of each. Never, by a slip of the tongue, have they so much as alluded to either of their old friends, any more than Miles has alluded to his expulsion…”” (Ch.7) 

The governess’s so-called proof is not proof, but “the systematic silence” of the children. To her, the silence means they know, they are accomplices, they’re hiding the truth. Does it though? 
And: 

““Why, of the very things that have delighted, fascinated, and yet, at bottom, as I now so strangely see, mystified and troubled me. Their more than earthly beauty, their absolutely unnatural goodness. It’s a game,” I went on; “it’s a policy and a fraud!”” (ibid.) 

With that silence is the children’s “absolutely unnatural goodness”, which doesn’t go with the fact that Miles has been expelled from school. To be honest though, the governess can contact the school and ask exactly why he’s expelled. That would save time guessing and making up stories. But then of course we wouldn’t have a story then. 
Now look at this: 

“They had a delightful endless appetite for passages in my own history, to which I had again and again treated them; they were in possession of everything that had ever happened to me, had had, with every circumstance, the story of my smallest adventures and of those of my brothers and sisters and of the cat and the dog at home, as well as many particulars of the whimsical bent of my father, of the furniture and arrangement of our house, and of the conversation of the old women of our village. There were things enough, taking one with another, to chatter about, if one went very fast and knew by instinct when to go round. They pulled with an art of their own the strings of my invention and my memory; and nothing else perhaps, when I thought of such occasions afterward, gave me so the suspicion of being watched from under cover. It was in any case over my life, my past, and my friends alone that we could take anything like our ease—a state of affairs that led them sometimes without the least pertinence to break out into sociable reminders.” (Ch.8) 

This reminds me of Ingmar Bergman’s Persona: the governess doesn’t know what the children think; she talks a lot about herself, too much about herself, that she becomes vulnerable and starts to imagine that she is being studied. Doesn’t that sound familiar? 
Let’s see where this is going.