Am I confused here or do the three points above seem to hold?

I think formally you are right.

But I think that if consciousness is essential to how we get important aspects of our input-output map, then I think the chances of there being another mechanism that works to get the same input-output map are equal to the chances that you could program a car to drive from here to Los Angeles without using any feedback mechanisms, by just dialing in all the stops and starts and turns and so on that it would need ahead of time. Formally possible, but absolutely bearing no real relationship to how anything that works has ever been built.

I am not a mathematician about these things, I am an engineer or a physicist in the sense of Feynman.