After listening to the segment, I think it's much less likely that any historical Jesus existed at all. Though I'm under the impression that there were itinerant preachers at the time, and that apocalypticism was a popular theme among them. Maybe voluntary poverty and nonviolence as well. So he could well be an amalgam of the type.
There is one thing that Christopher Hitchens pointed out that I found kind of interesting: the sheer amount of fabrication needed to get Jesus from Nazareth to Bethlehem may be significant; if Jesus was a purely fictional character, why not just have him born in Bethlehem and be done with it?
Thank you for posting the video - it's always fun to be reminded of Hitch.
As for the claim, that would make more sense if we are imagining Jesus was 'invented' in the same way that 'Don Draper' was invented - to fulfill a particular storyline, by a person (or a small group of people) who had a particular narrative in mind for him. All of the 'problems' that Christian apologetics needs to resolve only come about because of a later, larger structure imposed on the narrative, that would not have been there in the first place. On his way to becoming the Christian god and part of the trinity, Jesus would have gone through a number of identities - teacher; prophet; messiah (which in Jewish mythology was not equivalent to god); and perhaps some others that we have lost trace of.
My biggest problem with this sort of 'wouldn't you expect ...' argument for religion (eg "If he was made up, wouldn't you expect them to invent him as being born in the right place?") is that they are weaknesses being sold as strengths for no logical reason. As such, they're identical to the conspiracy theorists' "It must be true, because the fact there's no evidence here (or contrary evidence here) proves
that the evidence is manipulated by the conspirators". Starting with motivated reasoning (as Steve talked about, with regards Religion), and accepting both evidence and bad or missing evidence as convincing, you can literally prove anything.