That's not true. It is true that you must reasonably believe
that deadly force will
be used against the occupant(s). IOW, you don't have to be acting "in response" to deadly force; responding to a credible threat of it is enough, although you might have to ultimately convince a jury, in NYS, that the threat was credible.
Would I believe, if someone were to break into my house, that he represented a credible threat of deadly force? I'd have to decide, very quickly, in that event. I can say that I wouldn't discuss my decision, whatever it might be, with the criminal, and that if I decided that the threat were credible, he might well not be able to be a witness against me, thereafter. The best thing for him would be to stay out of my house, thus not forcing me to make a snap decision.
Or, he could just shine a flashlight on himself, to help me know that he's not armed. He probably wouldn't, though, because he wouldn't be breaking into my house to be of help to me.