Okay, I think I found what you're referring to.

First off, don't trust a single word that you hear in Zeitgeist.

That aside, though...the confusion here comes from ambiguous language. Zeitgeist apparently says "the fourth source [that is, for a reference to the life of Jesus] is Josephus and this source has been proven to be a forgery for hundreds of years." But it didn't mean to imply that Josephus himself didn't exist, or that his whole corpus of works was forged; rather, that this particular passage on Jesus in Josephus is thought to have been a later interpolation, not original to the text.

As for the passage itself: it's indeed been the subject of much scholarly debate for centuries. There's been a period in modern scholarship where many scholars have accepted that parts of the passage may be original to Josephus. However, there are also weighty arguments that the whole passage is interpolated, as well. We've had several threads on this on /r/AcademicBiblical.

I lean more towards the entire passage being forged. However, despite the extremely detailed work that's already been done on it, I still think there remains to be more work done.

No.

Josephus the Historian clearly existed, and that's not a matter of scholarly debate. He records his autobiography in The Jewish War, and how accurate his own account of his life is and his works are in general are a matter for debate. To my knowledge, no extensive historical work has been done on the matter of Josephus' existence because it is has never been a serious question within the scholarly community.

I would love to provide a source, but its rather hard to provide a source on the absence of discussion within the academic community.

*guerrilla (from the french guerre - war), not gorilla - though that sounds more interesting.

Please excuse my pedantic, tangential post.