> But you're not saying that the pencil is not broken, you're saying I can't see a broken pencil.
No, I'm saying you're inferring a false conclusion (the pencil is broken/we have subjectivity) from an inherently flawed perception (I see a broken pencil sitting in water/I perceive subjectivity).
For the sake of argument, let's assume the mental model of the paper I linked to. Our pseudo-perception of our own subjectivity is really a false conclusion we infer from a differential between the signal we receive from our perceptions of the outside world, with the signal from our internal model of ourselves perceiving the outside world. The constant switching back and forth as these signals consecutively dominate each other, combined with our slow perceptual response time relative to this switching, yields the illusion of subjectivity, similar to how a uniprocessor computer yields the illusion of real parallelism by context switching processes thousands of times per second. It's still just an illusion though.
> I'm not sure what distinction you're making? What would it mean for something to be "truly subjective"?
Subjective in the ontological sense, in that it cannot be reduced to an account consisting purely of third-person objective facts.
Certainly we perceive a type of "epistemic subjectivity" that's inherent to our distinct perspectives, but that's not true subjectivity in the ontological sense, like qualia.
> ...but I know I'm not a p-zombie. Even if I can't prove it to you, I know I definitely have subjective experience.
Materialistic theories of consciousness necessarily deny the conceivability of p-zombies, so you have nothing to prove. Any system with the same information processing structure as the model described in the paper (or whatever the "correct" model may be) would necessarily have consciousness. There is no non-functional "secret sauce" by which you can construct a p-zombie.