grammar - Negative questions: “No, I don’t” or "Yes, I don't"?

I’m an English teacher in Japan. Recently I ran into quite a conundrum, which I’m sure many others have struggled with. I was talking to one of my students in the presence of my boss and something my student said gave me the impression he hadn’t seen a particular movie. I then asked him, “So you haven’t seen the movie?” He responded, “No, I haven’t.” At this, I corrected him, saying he should say, “Yes, I haven’t.” My boss took issue with and said this is the number one thing that Japanese students learning English apparently trip up on, and traditionally they would be upset if I teach this kind of thing, because what they learned in school is that they should say, “No, I haven’t” in all cases. He has been riding me to find the answer for myself as to whether this is true or not, and while I’ve looked around online and found opinions, I can’t find anything “official”. And what bothers me is responding to a question such as “Have you not seen it” with “No, I haven’t” seems illogical to me, because then it sounds like it would be a double-negative; I’m asking if he has NOT seen the movie, so shouldn’t his answer be “YES, I haven’t seen it?” By saying “no“, to me it sounds like he would be saying, “No, I haven’t not seen it”, which would mean he has.

Also, the other night, my boss posed the example question on the board for me, “Do you not like it?”. Again, I would naturally think it should be, “Yes, I don’t” or “No, I do”, because I’d be affirming that question one way or the other.

He also showed me a place in a textbook we use with a question like “Don’t you like it” and the answer was “No, I don’t” or “Yes, I do”. This makes sense to me because the question is essentially saying, “I think you like it, right”, but I’d using a negative. Although when I think about it, why does this seem normal to me but it seems strange to me to say “Yes, I do” or “No, I don’t” to something like “Do you NOT like it”.

This thread seems to suggest I’m right: Proper yes/no answer to a question posed in negative form
My mom, who is really good with Grammar, also agreed with the responses in that thread. But I feel like I need something more official and concrete.

So could anyone tell me for sure what the right way is and if possible give me an official source, like a dictionary of sorts or something? Thanks a lot.