Similar experience. Judge made it clear to everyone that your options were:
Guilty: feel free to explain.
Not Guilty: Choose a date for your court appearance and don't forget to bring witnesses, evidence, lawyer (or have on appointed), etc.
I was doing 80 MPH on an empty freeway but it was 15 MPH over the limit. Of course I was guilty. But it was on the way to the airport where I was out of the country for 2 months so when the fine came via mail, then the collection agencies got involved...well, when I got back to 10 letters and a dozen voice messages, I just paid the collection agency not knowing any better (Hint: Never pay the collection agency -- deal with the police). When I finally got to court I said I'm guilty and here's why I was late paying. The judge cut my ticket in half, had the collection agency pay me back. Still had points on my license.
Another thing about standing before a judge. Try not to be an asshat. People try to stare the bailiff and judge down, be surly, etc. The judge isn't an administrative form. While bound by laws, the sentence is up to him. Be polite, joke around, whatever -- but try not to be a jerk unless he gives you cause, as he's the guy who's deciding whether to say "Thanks for being clear and honest, fine reduced to $30" or "Plaintiff will pay full fee".