Why did Abu Bakr not believe Fatimah al-Zahra in her claim that the Messenger had bequeathed to her, while precluding her dishonesty?

The report of Fatimah coming to Abu Bakr to request something the Prophet, peace be upon him, had gifted her is not authentically established. Rather, she came with Al-Abbas, both seeking their inheritance from the Prophet, peace be upon him, in Khaybar and Fadak. Abu Bakr then informed them that he had heard the Prophet, peace be upon him, say: "We do not leave inheritance; what we leave is charity," and that the family of Muhammad would partake from this wealth, and that he would not abandon any matter he saw the Prophet do but that he would do it.