I think I may be misunderstanding the context of the terms.
I suppose it's the State who "presses charges" in this case, but I believed that term was only used for the victim(s).
I'm thinking more along the lines that there is a clear cut victim of the alleged crime that refuses to file charges and the state does it in their stead. It would seem that the lack of charges from the alleged victim is the first defense of the accused, even the victim disagrees with the state.
But there are important reasons why one wouldn't press charges despite having suffered the crime; a few of the obvious ones include fear of retaliation, being unwilling to be in the presence of the perpetrator(s), lying to protect them, etc. And despite that refusal, there still may there be enough evidence to prove it happened.