I'm pretty sure this extends beyond ChatGPT.

The other day I meme-ified a photo with ChatGPT. Pleased with the style I fed that into Midjourney's "Describe" feature which aims to write an image generation prompt based on the image supplied. Midjourney did include a location as part of its output description and this was indeed accurate to the original photographic source material - this is all in spite of the image fed into the system being a ChatGPT-generated caricature, with what I thought was a generic looking background.

The lesson here is that these are still algorithmically generated images - and although it may not be obvious to us, even heavily stylised images may still give away a location through the inclusion of unremarkable landmarks. In my case it appears that the particular arrangement of mountains in the background was specific to a single geographic region.

While I think your story is entirely plausible, I wonder if there could be something else going on. Maybe ChatGPT puts the prompt (or an assumed location) in the image's metadata?

Generative AIs just patch together memorized data. So parts of the original data can sometimes get back out like victim's hairs out of a monster's mouth.