The finds indicate that the cave was used from the first century BCE to the first century CE (342).Now did I just read that right? Was this tomb already in use in the first century BCE? By my reckoning, that makes it a little more difficult for it to have been known as the special burial place of Jesus' disciples. Tabor and Jacobovici's speculation that the tomb belonged to the first century CE figure of Joseph of Arimathea also becomes unlikely in the light of this important detail.
After coming across this detail, I went to look at James Tabor's Preliminary Report and although he refers to that page of the book, he does not comment on this detail. It is implied throughout that this tomb is, without doubt, first century CE.
I have also checked through James D. Tabor and Simcha Jacobovici, The Jesus Discovery: The New Archaeological Find That Reveals the Birth of Christianity (New York: Simon & Schuster, 2012) and there is no discussion of the Kloner and Zissu's dating of the tomb there either.
Please correct me if I am wrong, but I would have thought that attempting to date the use of the tomb in question would be fundamental to any attempt to associate it with a particular group of people.