Josephus was writing in Judea less than a century after the fact, and grew up within living memory of it. Many historians agree that even though there is some later additions, the second reference to Jesus and his brother James appears to be legitimate.
The details are essentially impossible to verify, but what we actually have is four accounts taken from a variety of sources as well as other accounts that are not considered canon. These accounts are enough to assume that a person existed, even if we take almost all of what they say about him with skepticism. The Markan source, the Johanin Source, and "Q" are not working from one another, they appear to be three different accounts of the same set of events.