> This is not AI,

A little bit nitpicking, but according to books like AIMA that is indeed AI. In the first chapter even any control system is classified as AI.

Because of the reasons stated in the 1st chapter, I totally agree with the authors.

The whole system is AI. That part is a verifier in a chain of “suggestions/instict -> verifier” like used in neurosymbolic systems for automated driving, for example.