When dealing with officialdom, as with any similar situation, the argument has two protagonists, and some rules apply to both.
First - only start an argument that you know you have a reasonable chance of winning.
Second, make sure you know what your end objective is before you start, and keep on point throughout the argument.
Third - if you are going around in circles - walk away.
So - the council official got carried away with his desire to obtain details, and took it too far by involving the police.
The lady went around in circles, when her best option would have been to walk away.
Given that neither achieved any meaninful objective, both did well to keep their tempers, but it was always going to end up as an exercise in futlity.
I would have walked away after about a minute, and refused to entertain any further conversation.