Thanks, things are clicking with respect to the logic. I phrased it as a double negation but with the quotation marks you introduced it becomes a negation of the statement as a whole. Thanks for that, both you and Vaddha. I learned something new.
But thanks even more for bringing us back to the actual heart of the matter. I lost track of it myself. 
Who am I to say that I know what the Teacher would do? 
But what I’m saying is, the Kaccanagotta Sutta is not about refuting people who had notions of inherently existing cups. Nor do I see any other early texts that do such a thing.
So then, if I am right about the early texts, and if you are right that “Nagarjuna at least did think it important to refute inherently existing cups”, then he is extending beyond the early texts.
Which is not a problem! 
Maybe he had good reasons. I think he was refuting some post-Buddha Abhidharmic views myself, which is of course a common assumption.
Then secondly, the way I’ve seen it explained by others (since I’m not wise enough to interpret MMK myself directly) is that Nāgārjuna took the Kaccānagotta Sutta and particularly its statements on atthi and natthi to be about things in general, including cups. (Would you agree with that interpretation?)
Which is also not a problem! Maybe Nāgārjuna was doing something dialectical for good reasons, using the sutta creatively or what not.
But then people (I’m not saying people here) read the Kaccanagotta Sutta and import these later ideas (or similar) into it, as if they were already present there. But still, ALSO not a problem!
But then people (I’m not saying people here) go and teach others that this is what the text is really about, that this is what the Buddha was teaching too. There I do have a problem. Because then we dilute the Teacher’s message as I see it.
Just to clarify:
I’m saying that the Kaccanagotta Sutta is all about rebirth of the being (“world”), that the views of atthi and natthi concern views of post-mortem survival and nonsurvival (eternalism & one-life annihilation) of that “world”, and that right view concerns insight into this (as well as other related things, whereby the multiple-life annihilationism is also understood to be false).
This is not a widespread interpretation of this sutta, I think you’ll agree. 
But it is mine. (And the Pāli tradition’s, as I see it.) With this perspective you’ll understand what kind of interpretations I’m arguing against. Even if not directly that of Nāgārjuna, many people are indirectly influenced by him. Or have similar-enough ideas that I think I’m opposed to them all in the same way.
And then lastly, I think these differences matter not just textually, but for our practice too. Because I think the original message of the sutta is much more helpful in telling people whether they have right view or not. Which is of course it’s ultimate point.