<p>I think it was meant to be not 'not doing this at all' but 'not doing this with evil motive'. Something like affect or mood disorder. History knows examples when revengers under such mood disorders are found not guilty because they actually were of their mind  </p>

<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>

<p>In the trial, Jane is claiming that Timothy Carter didn't exist 5 years before that.   Carter appeared out of nothing.   So Jane's claim is he killed nobody who appeared 5 years before and was a serial killer. </p><p>I guess that's why the jurys' verdict was "not guilty." </p>