Josephus refers to Jesus in two places. In one, he says that James, the Christian leader in Jerusalem who was stoned, was "the brother of the Jesus whom they claimed was the messiah." That obviously is not a Christian insertion. The other passage has two interpolations that are easily spotted by anyone with experience of textual criticism or even just of using the apparatus criticus in Classical texts. The text runs (I'm quoting from memory — too lazy to look up the text and translate it! — and I've left out any punctuation as that would not have been used by J.):
"he was a wise man [if he was only a man [he was the messiah]] who performed strange deeds and taught many people on account of his teaching the leaders of our people made accusations against him and he was sentenced to death by the procurator Pontius Pilate after his death his followers did not lose faith in him and the movement called Christians still exists."
The square brackets mark the insertions and the order in which the were added, the first by a sympathiser, the second by a believer. They stand out because they don't fit the beliefs of J. or the flow of the text, so they couldn't have been written by Josephus. But the rest of passage must be authentic as a Christian would not have been surprised by the persistence of Christianity, nor would he have spoken of "our people".
The fact that J. was not a contemporary of Jesus doesn't mean that he was "parroting" things. If some-one born in 1980 wrote a book about Hitler, would you refuse to read it? It would be a secondary source, as opposed to a primary one, but sometimes secondary sources are all we have in history. There are no primary sources for Alexander the Great, for example.
