It is curious that the same people claim that the interpolator of this presumed (and today lost) passage about the causal link James/Jerusalem could even have the same construct: ''called Christ'' reffered to Jesus.
I translate their words:
(translated from CECILIA ANTONELLI , I FRAMMENTI DEGLI Ὑπομνήματα DI EGESIPPO, my bold)Bardy observes that although it is true that Eusebius, in 2,23,20, does not cite the source from which he has derived the alleged passage of the Antiquities, but he is usually very precise in the indication of his sources, this does not necessarily mean that Josephus spoke of James differently from the way reported in this passage, that is, "Ἰησοῦ τοῦ λεγομένου Χριστοῦ", for if the passage had been inserted by a Christian, that is, the possible interpolator, he would not refer to Jesus as to "he who is called Christ. " However, I think it can be countered that a Christian who would like to present the passage as authentically coming from Josephus's work may have included this construct in reference to Jesus precisely to make it more likely to attribute the passage to a Jew. Moreover, the same expression is also found in Antiquity 20,200, which is certainly authentic, and could therefore be borrowed by the interpolator from that passage to increase the credibility of the interpolation. Finally, the phrase is also in one of the Gospels, at the end of Jesus' genealogy in Mt 1.16, which proves that it is by no means impossible for a Christian to express himself in these terms about the Lord.
Note the very strange inconsistency: even in a note where a good suspect is raised about the real Josephus's use of ''called Christ'', that same suspect is removed rapidly only in virtue of the dogmatic ''authenticity'' -- ''certainly authentic'' -- of the same passage ''called Christ'' in Ant. 20:200. That and only that.