Have you ever actually read On Computable Numbers, With an Application to the Entscheidungsproblem? The whole point was to isolate the necessary components of what computers (which was a human job title at the time) do.
My point was that pen and paper, itself, is not a sufficient model of computation (it is not capable of any computation). Pen + paper + human is. The fact you mention is precisely why I chose to bring this situation up. If we throw in humans to the mix, our candidate "model of computation" can become heavily reliant on the capabilities of humans. At this point, we need to explicitly say that we include human interaction in this model. Based on my standards, this is not a really fruitful statement, since humans are almost capable of general computation alone. They just need the memory. Analogously, pen and paper is just a work tape. a work tape is not a system or automaton at all. I find it mind boggling that I have to explain this to people, especially those who appear so confident that they understand theory of computation.