If you mean people like me, and possibly other HNers, that like to occasionally look up FBI crime stats when there's news or talk about gun regulations, then yeah that crowd is likely to question ChatGPT outputs. But we're not normal, we're the minority.
The vast majority of people don't fact check anything they read online. The scary part about ChatGPT/AI is not the technology or accuracy, its the fact that there are so many people that will take its output at face value and others that will abuse that.