Wow, my opinion of the editing process at the New York Review of Books has just dropped, by a lot. It's not just that it's a bizarre claim, but that it's also stated so matter-of-factly. Honestly, the writer probably talked to a coder friend who uses an IDE, and the way the coder described auto-completion and type-checking extensions sounded very much like "self-correcting" code.
No matter what you think of difficulties of the Turing halting problem, I'd say that writers depend --and can benefit -- far more on "self-correcting" writing (particularly auto-correct) than programmers do on self-correcting code.
I think you're overreacting. The author could well be talking about neural nets, deep learning, etc. We may choose to nitpick or discuss the overall point.
No matter what you think of difficulties of the Turing halting problem, I'd say that writers depend --and can benefit -- far more on "self-correcting" writing (particularly auto-correct) than programmers do on self-correcting code.