I'm not even anti-AI. I use these tools all the time to make "zeroth draft" documents that I can build on. It actually saves me a lot of time! But everything is in service of me delivering products I care very, very much about getting right, and I don't assume their output is anything other than very sophisticated text autocompletion.
This might be a variation on one I've seen a few times: I'm an expert on something, and advising someone who wants to instead go with advice from their friend who isn't even involved.
(And who usually has little-to-no experience in the thing. But it's like calling up your nephew at Google to ask why your computer is slow. After the knowledgeable neighbor who looked at it already told them it's because they have very little RAM, and they're pushed into swap by this one program they installed. But the Google nephew hears "home PC slow", says they probably picked up a bunch of malware, and to reinstall Windows, and please stop calling during work hours.)
I think this can be a psychological quirk, or social dynamics pressure, or an inability to assess competence due to a lack of understanding of the field/subfield.
If I had to guess, I'd say the last one is probably the factor in being overruled by ChatGPT.
One end-run around that is to have some validation of your expertise in the decision-maker's mind, and it might be stupid. For example, in the minds of some decision-makers, if the person has some credential they value ("They went to MIT!", "They worked at Google!", "I'm paying out the nose for their consulting fee!") the decision-maker will put a lot more weight on that person. Maybe even more weight than they give the ChatGPT superintelligence they imagine. It's nice to be listened to, even if it's for the wrong reasons.