Is the story of David with the bird, and his observation of a woman bathing, and sending a servant to get to know her, true?

Some exegetes mention a story about David (peace be upon him) indicating that he saw a woman bathing and fell in love with her, so he ordered her husband to be killed in order to marry her. This story is among the Isra'iliyyat (tales of Jewish origin) that are not authentically reported from the Prophet (peace and blessings be upon him) and are not befitting the stature of Allah's prophet David. Ibn Kathir (may Allah have mercy on him) mentioned that most of the stories narrated in this regard are taken from the Isra'iliyyat, and no authentic hadith has been established concerning them. The Permanent Committee for Issuing Fatwas has affirmed that what many exegetes mention about the story of David (peace be upon him) falling in love with the commander's wife is incorrect, and it indicated that all these narrations trace back to the Isra'iliyyat and cannot be relied upon.