I voted to close the question because ELL isn't here to analyse the syntax of chatbots. Once four other users had agreed with me, it did get closed, but before that this is what I said to the OP in a comment...
...you shouldn't be treating ChatGPT as a "source" of English for learning purposes. You shouldn't even trust it to write syntactically valid English sentences in the first place, and you certainly shouldn't trust it when it starts explaining grammatical rules to you. It might be right (and it'll be getting more reliable day by day), but even ChatGPT (by far the "cleverest" bot around today) can make some ridiculously untrue assertions. More crucially, it can slip in critical, but non-obvious errors which might not always be noticed even by people who know the relevant "truth".
I didn't really engage with the specific usage being queried by the Neither do I question. I saw that the OP here in this meta question had posted a brief comment rejecting whatever ChatGPT supposedly claimed, so I just "upticked" that comment before casting my closevote as above.
We generally reject "limited scope" questions (name for a programming variable, audio transcription, lyrics interpretation,...). By which I mean the sought answer usually applies to exactly and only the specific "example" presented in the question.
If it's obvious that some question is only being posed because of something ChatGPT said, I think the only sane response is to summarily close it. That's not just if someone has found a situation where ChatGPT appears to be making false assertions - we should resolutely cull all questions asking for help understanding why ChatGPT says something.
Questions asking us to "explain" what ChatGPT says are potentially much more insidious (and invidious! :) than the similar ones we've always had prompted by "writing assistant" recommendations (MS-Word, Grammarly, etc.). At least with Grammarly, there's something "static" that you can pin down and analyze (if debugging other people's software is your bag! :)
With ChatGPT, even if you present it the exact same question / example / whatever, it'll give you potentially wildly different responses. It's bad enough we're the "dumping ground" for ELU's unwanted crap - ELL should not be thrown into the "black hole" of ChatGPT!
I may be a voice in the wilderness here, but I really do think if we allow ChatGPT so much as a toehold on ELL, it will eventually destroy the site. It's ironic that so far as I can see, this is likely to happen because one mod wants it re-opened. I could maybe accept if five high-rep users voted to re-open, but to let something as important as this go through on the say-so of a single mod seems a bit high-handed.