Not to be contentious, Twinkle, but these Bible stories fit many of the criteria of authenticity. One, they are reported at a time close to the time the event occurred. Secondly, they show the King in a bad light which would not necessarily be in the author's best interest were it not for its fundamental truth. Third, it fits the other known facts in this story, i.e., it is congruent. If the Jews don't have problems with their iconic King David being human, why should you?
Mandi