Agree that the study design is flawed. Going with the possibly-hallucinated AI answer is rational as long as you know the hallucination rate isn't 100% (or whatever % you get after factoring in the monetary rewards they introduced later in the study)

But in reality when google gives you the wrong answer, you at least have some signals you can use to infer confidence. For example, the number of results, whether the sources are trustworthy, etc.

AI at best tucks that away in a footnote and discourages further critical thinking.