So you weren't there, and you admit that the trooper made a judgement call, and could have left out important facts on the ticket, and you're telling them to admit guilt rather than having their day in court? That's some good advice.
edit: Oh, and add on the fact that they haven't seen the video and don't know exactly what's on it. But they still should just send in the fine and forget about it. Bare minimum -- have a lawyer look at the video.
I'm saying I wasn't there in order to find out exactly what happened. I'm asking if there is a video tape of the event, because if it exists, based on my experience with such evidence, they are screwed in any type of defense. Better in that case to talk to teh SA before the court date and ask for a lesser charge, and then beg the mercy of the court than to try to fight it, pay court costs and attorney fees on top of whatever fine is imposed and run the risk of additional charges being filed. That is my advice, take it or leave it.