The claims are made. I see the results from those claims. In Ezra's case, he reported the history of the repatriation step by step. He was there as an eyewitness. His account follows the course of general history as was handed down to us. But in this one instance he would lie?
Same goes for Josephus. He wrote up history to the best of his ability. But in this one instance he would fabricate the evidence by quoting myth. If you follow his writings, you will realize he was too proud to sully his reputation by publishing untruths or myths. He reported at the time that one could visit a tower Daniel had built which served as the burial place of kings. His countrymen and the Romans would have ridiculed him if he lied.
264 Now when Daniel was become so illustrious and famous, on account of the opinion men had that he was beloved of God, he built a tower at Ecbatana, in Media: it was a most elegant building, and wonderfully made, and it is still remaining, and preserved to this day; and to such as see it, it appears to have been recently built, and to have been no older than that very day when anyone looks upon it, it is so fresh, flourishing, and beautiful, and no way grown old in so long time;
265 for buildings suffer the same as men do, they grow old as well as they, and by numbers of years their strength is dissolved, and their beauty withered. Now they bury the kings of Media, of Persia, and Parthia in this tower, to this day, and he who was entrusted with the care of it was a Jewish priest; which thing is also observed to this day. (Ant 10:264-265 JOE)