The judge is the one who determines what's "proof". In the story, he decided that name & birthdate was enough to not dismiss the case. She could have hired a la

The judge is the one who determines what's "proof". In the story, he decided that name & birthdate was enough to not dismiss the case. She could have hired a lawyer and spent time fighting the case and maybe won, but she wanted to get it resolved immediately and a guilty plea is the only way to do that.