I believe that James and Jesus were siblings, one way or another, is soundly refuted by the Church.
Who is to say that Josephus didn't get that part wrong? He obviously wasn't terribly interested in Jesus anyway, as he only devoted a couple of lines to Him.
A matter of trivia and interpretation that certainly would have no impact on whether or not Jesus was the Messiah --- all that is necessary for fulfillment of prophesy was an initial virgin birth. Scripture says nothing about afterwards.
For what it is worth, most protestant denominations opt for the literal interpretation of the Greek words used ("of one womb") and opine that James was Jesus's half brother.
Whether they were brothers or cousins is irrelevant to the subject. If brother was mistranslated from the OT it is highly likely that it was also mistranslated from Josephus.