THEN, after calling them up and explaining the situation, they apologized and said they’d dismiss the charge–which they failed to do

That sounds about right. When I was in college I got a speeding ticket halfway in between the college town and the city my parents lived in. Couldn’t afford the fine due to being a poor college student, and called the court and asked if an extension was possible. They told me absolutely, how long do you need, and then I started saving up. Shortly before I had enough, I got a call from my Mom that she had received a letter saying there was a bench warrant for my arrest over the fine