Should such answers be deleted/flagged?
A post with unattributed content from a bot is plagiarism and should get flagged for immediate deletion.
The rest of my answer assumes proper attribution.
What if the post is generated by an AI but checked for accuracy by a native speaker?
Let's take a step back first to what FF actually did, which is to provide a bare quote of what ChatGPT said without any other framing context, that's to say, with no stated support for the content. This kind of answer has no place on ELL or the SO Network at large.
Any learner who wants a direct answer from ChatGPT can install the browser extension or get an OpenAI account and ask the bot themselves. The reason people continue to ask questions here is that, for better or worse, they want answers from humans. A bare quote of an answer from a chat bot is roughly on par with a bare quote from an answer on Quora or Yahoo Answers. None of those sources are at all reliable, so merely quoting what they said doesn't even qualify as an answer in my books, and should be flagged as "not an answer" and deleted.
Now, back to OP's actual question. If FF had said they'd verified and approved of the content of ChatGPT's answer, then FF would be asserting the content as their own answer, though in someone (something?) else's words. This is a value-added version of a bare quote as it comes with the explicit approval of a high-rep user with a positive history of answering questions.
I'm divided on whether an explicitly supported AI bot quote is acceptable as an answer, and leaning heavily (please, please) towards unacceptable.
I can support it in that it's roughly equivalent to saying, "The answer is 'Yes'. User123 said it perfectly on Quora:...", which we do allow here.
But I also oppose it because it may reasonably lead to a flood of answers from people who claim to have carefully read the content, but in fact have not. Finding the exact answer the user is looking for on a site like Quora requires some labour and luck. You cannot build a high-rep account by Quora-mining. You could, however, build a high-rep account by posting unverified quotes from AI bots, but claiming to have verified them. Modding this behaviour would be be nearly impossible. The easiest way to deal with this is to ban AI answers altogether.
What if the post is a correct answer?
This is irrelevant. We don't deal in correct or incorrect answers on this network, only upvotes and downvotes. Correct answers will generally get upvoted and incorrect ones will get downvoted. But anyone with a couple months' experience here knows that a highly upvoted answer can attract an expert who shows that it's not correct after all.
What if the question is about text produced by an AI?
Questions about AI-produced English or AI-produced statements about English are just as valid as those produced by native speakers, English teachers and English student classmates, all of which are welcome here. In other words,
ChatGPT says X. Is that good grammar/true?
is as valid a question as
My friend says X. Is that good grammar/true?
Not asked, but I'm answering it: What if the language of the question itself is generated by an AI bot?
While I wouldn't delete a question if the asker used AI to help them phrase it, I would strongly discourage it because a learner couldn't be sure it says what they think it says, and might assume that because a bot made it, it's perfect.
The trouble I see is people gaming the system by telling ChatGPT things like, "Write a hundred questions typical of ELL" and posting a few every day and building rep. Even with attribution, this violates the intent of the site, which is to help learners, not to generate question content. Since there's no way to determine whether a user is of this type or of the type in the paragraph above, I think we need to ban all questions written by AI.
By banning all questions and answers generated by AI, we're not depriving anyone of anything, we're keeping closer to the purpose of this site, and we're making our lives easier, so I support a blanket rule of no questions or answers generated by AI. (This wording fully allows for questions about content generated by AI)