It's not just cops. I almost did this on a friend who was making increasingly shrill suicide threats. We have patient's bill of rights, so our state errs on the side of the patient.
But in this case, there was nothing wrong with this poor woman, he did it out of misogyny.
Authorities are required to investigate before committing someone. They don't just take any asshole's word for it. People pranking social and police services, including calling out SWAT to break into your home (called swatting), is becoming so much more prevalent that it is now a separate criminal offense. They used to be charged as misdemeanors but the more serious ones are now classed as felonies with significant jail time attached.