In the interview, Price discusses the sparse evidence for Jesus. He mentions the passage from the Jewish writer Josephus that talks about Jesus and his brother James (Jewish Antiquities, 20.200, quoted here from Wikipedia)
...so he [the high priest Ananus] assembled the sanhedrin of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done....Now, I have read several scholars who have addressed the evidence for Jesus, and this passage is generally considered an authentic reference to the Jesus of Christianity. Price, however, makes a startling claim:
"If you look a little farther, it says that James and Jesus were the sons of a guy named Damneus, and that they were candidates for the high priest - it wasn't Jesus of Nazareth at all!"
So, what's the story here? Have all those other scholars simply missed the fact that this Jesus was the son of Damneus and a candidate for the high priesthood? Well, here's how the rest of the passage runs:
...they also sent to the king, desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrin without his consent. Whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him, when he had ruled but three months, and made Jesus, the son of Damneus, high priest.Note that, contrary to what Price says, there is nothing here about James being a candidate for the high priesthood, or being a son of Damneus.
Notice too that the earlier passage mentions "Jesus, who was called Christ," whereas the second passage identifies "Jesus, the son of Damneus." Price doesn't say why he thinks these two are the same person; it certainly isn't implied by the text. "Jesus" was not such an uncommon name: a little later, Josephus mentions that Jesus, the son of Damneus, was succeeded as high priest by Jesus, the son of Gamaliel. It seems more likely, in fact, that "Jesus, the son of Damneus" is being distinguished from "Jesus, who was called Christ."
Now, Price is giving a web interview, not writing a scholarly paper, and perhaps he has something more complicated in mind. Earlier in the interview, Price discussed the other place where Josephus mentions "Jesus, who was called Christ" (Jewish Antiquities, 18.63-64). Price points out that Josephus himself considered the emperor Vespasian to be the Jewish Christ/Messiah (a bit of flattery from Josephus to his imperial patron), and so was unlikely to use "Christ" to refer to anyone else. Maybe Price thinks that "who was called Christ" was missing from the original text, and inserted later by a Christian author. (This is similar to what many scholars think happened with Jewish Antiquities, 18.63-64. You can read about it in the Wiki article.) But then, what would have originally been in its place? Perhaps "Jesus, the son of Damneus", as it appears later? But, if Josephus had already identified this Jesus as "son of Damneus", why would he need to identify him again? Why wouldn't he just say "Jesus"?
For comparison, look at 20.197:
As soon as the king heard this news, he gave the high priesthood to Joseph, who was called Cabi, the son of Simon, formerly high priest.
Here Josephus identifies Joseph as "the son of Simon." But in the next chapter, Josephus continues
But the king deprived Joseph of the high priesthood....
Here, once having identified which Joseph he was talking about, he just refers to him as "Joseph" without any other identification. So, if "Jesus, the son of Damneus" was what Josephus originally wrote, then we would expect "the son of Damneus" would not be needed in the later position if it were the same Jesus that became high priest.
So I can't make any sense out of Price's claim that the James who was stoned was the brother of Jesus, the son of Damneus. Perhaps Price has argued this all out in some scholarly article. But it seems to me to be a case of choosing the interpretation that fits your preconceived outcome, rather than the interpretation that makes the most sense.
This may seem to be too small a point to be worth all the verbiage - but it makes me cautious about everything he says in the interview. If he is willing to play fast and loose with the text here, how reliable are his other claims?