That was ChatGPT-4 speaking there. It knows a lot more science than I do. I do not think it misspoke, but they do say it can make mistakes.

However, your perspective is correct but also in agreement with ChatGPT-4. Since the light took 13.4 billion years to get to us, if we see it as it is today minus 13.4 billion years, that means the object is 13.4 billion years old.

If we see the light as it was 13.4 billion years ago reaching us today, that still makes the object 13.4 billion years old.