“Truth” is not owned by anyone in the same way that the definition of a “Faithful” is not owned by anyone. It is a concept with a longstanding fairly agreed upon understanding.
Imagine you being little again and your Mom discovered that someone got into the cookie jar. You tell her the dog ate it. When your Mother, seeing chocolate chip residue on your cheek, told you to tell you the truth, you both knew that what she wants from you is a sentence that matches up with what happened. So you tell her the truth – you ate the cookies (and not the dog, as you had try to convince her of earlier).
So the statement that you ate the cookie is true – what it claims in the sentence matches up (corresponds) with what happened earlier (reality).
Who owns that truth? No one. You cannot own it. You can agree with it or deny it. If you deny it, doing so doesn’t take away the truth value of the sentence. All it does is show that you are ignorant of the claim or reality, that you don’t want it to be true, or that you don’t want to face the consequences of it.
Does this make sense to you?