In Smyth, there's 2760, etc. on accumulation of negatives. My understanding is that the basic rule is that compound negatives reinforce previous negatives in the same clause, but otherwise they have their own negative value.
I think the difficulty in this example is a different issue just because it doesn't seem like the negative makes a difference. Even in English, for example, I could say both
there is no one who will be saved, either when opposing you or any other people
there is no one who will be saved, neither when opposing you nor any other people
To be honest, I don't understand what's going on here with this negative (in any language). (That οὐδενί is a negative reinforcing οὔτε however does follow the above rule.) I hope it's clear what I mean.
But I don't think there's anything special about this construction in general with respect to negation. I'm sure, although I can't find any examples, that you would have
οὐκ ἔστιν ὅστις οὐδὲν ἐρεῖ = everyone will say something, not everyone will say nothing
With the simple negation, though, I know it's true that ούκ ἔστιν ὅστις οὐ = everyone.