How do you know those two statements are true? It looks like you are assuming an HJ then trying to find texts to prove your assumption.
Well given how many Messianic pretenders were running around it seems a safe bet that if Jesus did exist he would have been regarded in this vein.
I should mention that Carrier's minimal Historical Jesus doesn't require that Jesus was killed by The Powers That Be but that his followers
claimed that this was true. So Craig B's two criteria aren't that far off from Carrier's three criteria:
1)
An actual man at some point named Jesus acquired followers in life who continued as an identifiable movement after his death
2)
This is the same Jesus who was claimed by some of his followers to have been executed by the Jewish or Roman authorities
3) This is the same Jesus some of whose followers soon began worshipping as a living god (or demigod)
As I said before there are places where this fails but you do NOT get the Jesus myth but the
ahistorical Jesus ie "no historical Jesus in any pertinent sense".
Several examples of this are:
* John Robertson's 1900 idea that the Gospel Jesus was a composite character or that a person inspired by Paul's writings took up the name Jesus, tried to preach his own version of Paul's teachings, and got killed for his troubles.
* The idea expressed by Remsberg that there was a Jesus but his following wasn't an identifiable movement until Paul and later the writers of the Gospels got a hold of it: "Jesus, if he existed, was a Jew, and his religion, with a few innovations, was Judaism. With his death, probably, his apotheosis began. During the first century the transformation was slow; but during the succeeding centuries rapid. The Judaic elements of his religion were, in time, nearly all eliminated, and the Pagan elements, one by one, were incorporated into the new faith."
* G. A. Wells' Jesus Legend (1996) on with its mythical Paul Jesus + 1st century teacher who was not executed fails point 2 (they are not the
same Jesus) so by Carrier's criteria is NOT a "historical Jesus in any pertinent sense" (This does explain Carrier's classification of this work as 'ahistoricitical')
* Dan Barker's "Other skeptics deny that the Jesus character portrayed in the New Testament existed, but that there could have been a first century personality after whom the exaggerated myth was pattered." (2006 Losing Faith in Faith pg 372) would also fail Carrier's criteria as Baker's first century personality need not be named "Jesus" or if he was his movement was not identifiable until much later.
So failing one of Carrier's three historical criteria does NOT necessarily result in the Jesus Myth theory but it does result in the
ahistorical Jesus theory.