Option A says (or assumes) that there is an “objective” reality out there, and a person approaches it with sensory tools that supposedly help him recognize that reality. Then the question, it seems to me, is whether the information received through those tools actually describes objective reality correctly—or more precisely, whether I trust the tools to describe objective reality correctly.
Option B asks whether these tools work at all, functioning on the technical level regardless of whether they are actually faithful to the facts they produce.

Assuming that when you speak about trusting the tools you mean something more like Option A, because Option B is pretty banal, the question is how one can even talk about the likelihood or unlikelihood that the tools are faithful or unfaithful to “objective reality,” since we have no access to it without those very tools. So how can one even speak about my view on whether I do or do not trust their reliability? And if so, the argument collapses.

K, I think the Rabbi would say that this is simply a foundational assumption, and you need to examine yourself and ask whether you in fact believe it or not, and that’s it.
Every argument is built on foundational assumptions. Here it only serves as a kind of self-test for you.
But it’ll be interesting to hear what the Rabbi says.
(By the way, specifically B may be connected to A.)

You’re repeating the same formulation, and I still don’t understand the difference between the two possibilities. Cognitive faculties that don’t work are faculties that do not give me a reliable picture (one that corresponds to objective reality).

Rabbi, perhaps K was asking whether there might be cognitive faculties that work but do not reflect true reality.
Suppose you take the theory of the four elements—it works, but not well enough. And likewise Newton, who improved things. But in the end these are only approximations.