Turing was simply describing what people do: in a math test, I give you a problem, you solve it - without cheating, that is, interacting with your environment - using an algorithm, you hand it back to me. He idealized what a human does - infinite time and memory -, and then, as a final step, he said: "A machine - also idealized - can do that." The important thing is that in the definition of what was later to be called "Turing computability", interaction during the computation is verboten.