If I post a please-email-me outside of a Show HN thread, it might be anything! but the most common reason is that I want to send them a repost invite for some cool article they posted long ago. Invited reposts make it into the second-chance pool (see https://news.ycombinator.com/pool and https://news.ycombinator.com/item?id=26998308).
A priori, there’s no reason they couldn’t include their own GPT model that also lives on your own server.
[0] https://en.wikipedia.org/wiki/Generative_pre-trained_transfo...
Regardless, a GPT model is not a proprietary technology you must get from OpenAI. You’re right that this tool uses OpenAI’s API, but this isn’t necessarily implied by the use of GPT.
BTW you answer structure is very similar to ChatGPT’s when you point it to a mistake.