Good point, and we really don't know what all else is going on here. Public humiliation may work, or it may not if she is already humiliated for other more personal reasons. Ultimately, the girl will do better or worse, depending upon ALL of her experiences. I don’t know why people were so upset about her having to hold up a sign, though.
As for the blame game, I agree that parents shouldn't just up and blame teachers for the behavior of their children. Instead, they should take responsibility and find out what ALL is going on that they don't know about. Children don't just act out without reason. It very well may be something that they are doing, or not doing, and they are just too blind (or "too busy") to change their own behavior.
And about the prisoners, many of the most troubled children already have relatives and friends locked up. For them, their neighborhoods are as dangerous as prison itself. They are surrounded by criminals daily, so what is any communication with another one going to do... unless that prisoner has actually turned his life around? What is threatening them with jail going to do, when they full expect to end up there anyway? Or, they simply expect to end up dead before their 24th birthday? I am not a fan of those programs, because I view them as an attempt at a quick fix to a much more complicated problem.