Here is an article by Anthropic that explains what they do and mean in more detail: https://alignment.anthropic.com/2025/honesty-elicitation/
When they say "Honesty" I don't think to myself, "Goodness, does this model have moral understanding?" No, I understand they mean it's less likely to directly bullshit me, which models frequently do.
I don't feel like this level of pedantry around language is useful for people who more or less know what's going on with LLMs. (Again, I concede that perhaps with a less technical audience, there's more need for it.)