Josephus wrote a century later, only a couple of lines he wrote himself.  What little he wrote was added to and it was taken straight out of the Gospel of Luke.  Obviously, Josephus witnessed nothing of Jesus, nor could he have witnesses available to him.  It is not a question of whether Pilate and Herod were historical figures.  What is in question is whether each were deployed accurately in the Gospels.  Pilate was sadistic, cruel and quick to execute, yet in the Gospels he is presented sympathetic.  Many works of fiction note historical events, but the story itself is not historically verified...the Gospels as I wrote are not historically verified.  That does not mean Jesus did not exist.  It means the Gospels were written by unknown writers, who never witnessed Jesus, but wrote with an intent to convince a particular audience...no intention for accuracy.  Historical-critical is a valid attempt to know.  What ought to be said;  we simply do not know with certainty.