The statement only refers to "what is true", not your situation; each pronoun refers only to "what is true":
"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.
"What is true" does not refer to the entire universe. In "owning up to it doesn't make it worse", it refers to the specific thing "what is true" that you are trying to change your mind about. "Owning up to P doesn't make P worse", because your state of mind is not causally connected to P. In the specific example of finding that X is false:
"X is false" is already true. Owning up to it doesn't make "X is false" worse.
Clearly whatever bad things are brought about by a state of affairs where X is ...
—Eugene Gendlin