By that logic you might as well say a piece of paper, or this text input box, is Turing complete, since a human can execute a Turing machine on it.
This is not that different from the Excel example: the system displays Turing completeness if supplied a clock as input (a person clicking a button in the spreadsheet, for instance). The human is not making any decisions in this case - the logic manifests itself entirely from within the system.
A piece of paper is not Turing Complete because the computation happens in the head of whoever is holding the pen.
An excel sheet (or actually a power point presentation!) is, because the user just has to mindlessly, unconditionally, do a simple, non computational action to make the cycles go forward.
There is a difference between the two scenario, and if you can't see it, please do ask questions until I'm able to make that clear to you.
You don't have to turn this into a philosophical problem that will inevitably pitch hypothetical GAI against menial workers, thousand monkeys on a typewriter, or equivalently a young person and billions of neurons on blank canvas. That's not anymore about the technical point of the submission. It would need back up from psychology to remain remotely technical: why did the chicken cross the road?
Lambda calculus emulates a computer (a human that computes) with an infinite pencil and infinite sheet of paper.
This is taken, if I remember correctly, straight from the communication between Church and Turing.
So, the logic is correct. Human can execute Turing machine and Turing machine (and lambda calculus) were invented to formalize the notion of human computers.
Also DFA has no looping as in "doing infinite computation steps over finite input".
By using Peano Axioms? Now wait a minute!
Yes, and if you read through the pieces of paper that make up the articles that described Turing copleteness you’ll realize that they don’t talk about mechanical machines but about mathematical and local systems. Moving rocks in the desert according to fixed rules can make up a Turing complete system, as can markings on paper.