Of course I assume that other people are concious, but I am nonetheless capable of imagining a person who is not. And the point isn't whether such a thing is p

Of course I assume that other people are concious, but I am nonetheless capable of imagining a person who is not. And the point isn't whether such a thing is physically possible in our universe, merely that being able to conceive of such a thing identifies the distinction we're drawing. There is a notion of experience separate from the physical process that may cause it, because for any such process, we can imagine a world where it does not actually experience anything.