You're conflating what ChatGPT does with fact checking. It's as much a fact checker as a human is a fact checker. It's not their purpose to be either a grammar

You're conflating what ChatGPT does with fact checking. It's as much a fact checker as a human is a fact checker. It's not their purpose to be either a grammar checker or a fact checker, so you can't make assumptions about the models they have just yet. You can instruct a human to do fact checking, just like you can instruct ChatGPT to do it. You can instruct ChatGPT to structure text. Have you compared its output in both cases? Does it affect both parameters the same (from what I've seen, I don't expect that)?