It's an LLM. All it's supposed to do is generate output that fits with the given input. There isn't some logic in it that makes sending an email an error, or anything that enforces detecting any kind of error. You can wrap it in other tools for that, but there isn't any indication that's the case.
More than that, the initial post says the user found out about the email and then queried the LLM, so it didn't detect anything. There isn't any bug here, this is how LLMs operate.
Edit: here's a podcast discussing exactly this: https://youtu.be/RoIjWGi-w5o?is=2ly14A2UdKalHuAH
I pay for games instead of pirating because I believe that the people that worked on a game deserve to be compensated for their work. If these people are using generative AI that was trained with images obtained without the consent of the creators (and right now it's very unlikely they are using ethically-trained generators), they are not paying the artists that helped create their images. Why should I pay for the game then?