Josephus fought the Romans himself, personally. He literally lost to them, personally. He was a commander of Gallilian forces in the first Jewish-Roman war and was defeated in battle by Roman forces.
He was the loser. He wrote his history from that perspective.
Yes the Romans made him a citizen and gave him a pension. They routinely did that for adversaries they respected, plus he probably (though not certainly) handled some negotiations for them later in the war. They did not however commission or oversee his historical work. It is a history by someone who lost. It's notable in that it criticizes both Romans and Jews in some ways and praises both Romans and Jews in some ways. It is, like all good history, somewhat favorable to both sides. Unfortunately people expect a history done by someone who lost to be a flaming rant against the people they lost too, but that is not how good history is done.
Similarly minor aboriginal groups that have kept up their history tend to be critical of Europeans in many ways, but they also note the good things that where brought and sometimes make note of good Europeans that actually made good deals and dealt fairly with them. Histories of civilizations that 'lost' continues to be purveyed such as Aztec histories. Even when the victor does write the history they often write favorably about their opponent, and do not (or at least did not, in past centuries) routinely deride their credibility.
Historians write history, and they come from many different backgrounds. Unless you have unified public 'history' that everyone is forced to learn and is supposed to make ones own country look good there is no real use in 'winners bias'. Certainly every writer has their own bias, but even when a 'winner' writes it it can be just as bias against the 'winners' as 'losers'. Some elements of North American history classes are downright anti-European.
If you've read so much history you should see you're parroting propaganda, not the reality of histories as they are.
Then you take that propaganda and apply it to a story about David, who didn't even write the work we're considering. Moreover the work itself happily points out Davids flaws...