Or maybe they didn't train it that way to be manipulative (although it's certainly a plausible explanation) but simply as an accidental artifact of trying to make it give honest answers?

LLM-generated images sometimes includes text from the prompt as literal text in the image, so perhaps this is the same sort of artifact? If they've told it to be honest, it responds by talking about being honest instead of actually being honest, because it has no actual understanding of anything.