This is why you cannot detain someone that part is wrong no doubt. In my mind, if the weapon is coming out of the holster it is going to be because I plan to use it. Not because I plan to intimidate someone into submission, same thing goes for warning shots. Telling the cops "well I only meant to scare him when the gun accidentally went off" is one sure fire way to get into legal trouble.
On the other hand, if someone comes up to me, while I am minding my own business in a parking lot and says "people like you should be shot" then proceeds to begin shoving me(assuming the guy without the gun started it)...yeah I am going to feel threatened.
We do not have enough details but if the concealed carrier(Chris Williams) was NOT the one to initiate the physical contact(shoving) then the only thing he did wrong in my mind was to detain someone.
I don't know much about NM law but I know that if someone in Florida had come up to me, confronted me, threatened me with being shot(arguable) then shoved me I would have been within my legal rights to use my weapon.
Funny story on political bumper stickers though. For a while as a joke we were putting magnetic Pro-Obama magnets on each others cars during the 2008 election. Well one day I am driving down the highway when a car pulls up next to me, proceeds to honk his horn and then flip me off...ok that was odd....not 1 min or 2 later someone does the same thing but waves very friendly towards me.....ok that is REALLY weird. When I got to my destination sure and heck someone had put a giant Pro-Obama magnet on the back of my truck.