I think he’s treating intuitions as providing epistemic access to the moral facts
I think he’s treating his intuitions that way. He does not seem to be treating intuitions in general that way, since he doesn’t address things like how throughout most people have had the intuition that treating the outgroup poorly is morally good, nor how I have the intuition that it is immoral to claim access to moral facts.
That’s fair. I suppose that I was attempting to translate his statements into something that I could understand rather than taking them literally, as I should have.