The way I see it, the argument comes down to an assertion that as impressive as these technologies are, they are a local maximum that will always have some limitation that keeps it from feeling truly human (to us).

That's an assertion that has not been proven one way or the other. It's certainly true that progress has leveled off after an extraordinary climb, and most people would say it's still not a fully general intelligence yet. But we don't know if the next step requires incremental work or if it requires a radically different approach.

So it's just taking a stance on an unproven assertion rather than defining anything fundamental.