In that case saying "Owning up to the truth doesn't make the truth any worse" is correct, but doesn't settle the issue at hand as much as people tend to think it does. We don't just care about whether someone owning up to the truth makes the truth itself worse, which it obviously doesn't. We also care about whether it makes their or other people's situation worse, which it sometimes does.
5TimFreeman
"What is true" includes everything about my situation. Whether the truth is better or worse is a statement about my judgment of goodness of the truth, which surely includes my judgment of my situation. Whether I own up to the truth has immediate consequences on my situation, unless I can cheaply suppress behavior change deriving from that knowledge.
On the face of it, what you're saying seems to be obviously false. It's more likely that I misunderstand you somehow, but I can't imagine how right now.
You're conflating something here. The statement only refers to "what is true", not your situation; each pronoun refers only to "what is true":