Actually, a two week psych detention is pretty common where I live. Police are not equipped to deal with wild hares, and the alternative of throwing them in jail is harsh and may not get help to those who need it.
In effect, they are put in a county hospital rubber room, checked to make sure they are not having D.T.s or hallucinations, or having overdoses. They make an effort to find out if they are prescribed anti-psychotic drugs. etc.
Not bad for cops that have guns, tasers, and radios as their problem solving tools.
County psych are like a nice hospital ward. When they are coherent they can use the phone. If they have money they can order delivery pizza. They want it to be stress free, and to help those who need and want help.
I know they put people in psych wards for observation.
Highly unlikely for some lady who was a pain in the ass to a workman, or even to the police.
I believe they have to have reasonable belief the person could be a danger to themselves or others.
Being a pain in the neck does not meet that standard.
If her call was abusive, I could see her receiving a fine.