You are more than correct.
I have been the victim of such false allegations and been investigated by both police department detectives and DCS caseworkers. When the matter was before the court, I had both the detective and the caseworker present because they were willing to testify that the whole thing was a lie. It was a custody matter and they had also interviewed my daughter who was 7 at the time. The judge could not find me guilty because there was no evidence, but, because she knew that the state's own professional investigators were prepared to testify that a false report had been made, she would not even allow them to testify. And then she verbally abused me saying that I had just been "lucky" this time.
People actually wonder why so many men have no respect for female judges! Or why we discount all these reports of "domestic violence"? It's because women use this as a tactic to gain an advantage in divorce proceedings and the courts allow it every time.
I had a recent inquiry about donating some professional talents to the renovation of a "battered womens" shelter and, although I wasn't stupid enough to come right out and say it, I have no intention of contributing to this kind of thing when all too often it's simply used as a ploy in a court system that gives all the credence in the world to any allegation against a man, even when the proof of it being false is right in front of the judge's face.
Well, I have worked with battered men for many years, and not only are the women's shelter being not helpful to those men, I have instance where people associated with those groups KNOWINGLY assisted with false accusations. So, when I am solicited for anything for those groups, I tell them exactly what my experience is and exactly why I will not support them. I mean, why keep this shameful thing a secret? That is what dysfunctional families do.