<p>Jane is being tried for <i>murder</i>. For whatever reason the prosecutor (Ardilez) doesn't present the jury with any other options for their verdict (e.g. manslaughter) during the trial. Maybe he thinks Jane's crime is so obviously murder that other options are unnecessary - certainly the dialogues between Ardilez and Bertram imply they both think a guilty verdict is a foregone conclusion.
</p><p>However Jane convinces the jury that Timothy Carter was Red John. The jury decides that, because of this, shooting him dead was not murder. Maybe if they had been given the option they might have given a manslaughter verdict. However the only option is either guilty of murder or not guilty - and so they deliver a "not guilty" verdict. Juries can be capricious like this!
</p>