Origen never claimed that Josephus had written anything about the biblical Jesus. Origen wrote that Josephus had mentioned James the Just, and it was Origen that added comments about James supposedly being the brother of the biblical Jesus and did not say anything about Josephus writing about the biblical Jesus. Josephus was not one of the Messianic Jews who believed that a Messiah was supposedly going to come to save the Jews, which led to Origen writing that Josephus did not believe in anyone being the "Christ". For more information on what Origen had to say about Josephus see:
Origen on Josephus.
Why should we believe that Origen added the part about Jesus being the brother of James, instead of believing that it was in the original text of Josephus? If we compare what Origen stated, and what we see in Josephus, there is no reason to assume that Origen had to add something that was already present in the work of Josephus.
And Josephus, mentioning Jesus, and even saying that he is the so called Christ, would not in anyway make him accept Jesus as the Messiah. By calling Jesus, the so called Christ, it is actually showing that Josephus did not accept Jesus as Christ, Messiah, but instead is only referring to what others have called Jesus. In fact, Christ, by that time, was already becoming nearly a second name for Jesus, so it would be a good way for someone to identify Jesus. As we see no one else being called Christ, it would have been suiting for Josephus to state that Jesus was called Christ.
Back to Origen. I am not saying that it is a definite thing that Origen quoted from Josephus about Jesus, as there is no direct quote. However, when comparing the passage in Origen with the passage in Josephus, it certainly looks like a paraphrase by Origen. And the fact that Origen addresses the passage, in the same manner as Josephus did, by stating that James was the brother of Jesus, there is no reason to assume that Origen simply added it to his account.
Really, if we see Josephus stating that James was the brother of Jesus, and then Origen paraphrasing that section, and saying that James was the brother of Jesus, why should we assume that Origen added something to his account, when it was already present in the account he was paraphrasing from? It simply doesn't make sense.