I don't think this is a remotely accurate characterization of what happened. These engines are trained to produce plausible sounding language, and it is that rather than factual accuracy for which they have been optimized. They nevertheless can train on things like real world facts and engag in conversations about those facts in semi-pausible ways, and serve as useful tools despite not having been optimized for those purposes.
So chatGPT and other engines will hallucinate facts into existence if they support the objective of sounding plausiblel, whether it's dates, research citations, or anything else. The chat engine only engaged with the commenter on the question of the date being real because the commenter drilled down on that subject repeatedly. It wasn't proactively attempting to gaslight or engaging in any form of unhinged behavior, it wasn't repeatedly bringing it up, it was responding to inquiries that were laser focused on that specific subject, and it produced a bunch of the same generic plausible sounding language in response to all the inquiries. Both the commenter and the people reading along indulged in escalating incredulity that increasingly attributed specific and nefarious intentions to a blind language generation agent.
I think we're at the phase of cultural understanding where people are going to attribute outrageous and obviously false things to chatgpt based on ordinary conceptual confusions that users themselves are bringing to the table.