How can Al-Bukhari and Muslim narrate from Uthman ibn Abi Shaybah despite proof of his ridiculing the Qur’an, and from Ismail ibn Abi Uways despite his confession of fabricating Hadith?

The traditionists from whom the Two Shaykhs (Al-Bukhari and Muslim) narrated are of two types: first, those whose narrations they relied upon for fundamental principles, and whose narrations are sound (sahih) or good (hasan); and second, those from whom they narrated for corroboration and consideration. These narrators might have had some issues with their memory, but they had crossed the bridge (i.e., their status was established), so they are not abandoned unless there is clear proof. Al-Bukhari and Muslim narrated from some weak narrators whose weakness did not reach the extent of rejecting their narrations. However, they only narrated from them what was sound (sahih) from their narrations. The soundness of a weak narrator's hadith is known by its agreement with that of other trustworthy narrators (through corroborations and supporting evidence), and by reviewing his original sources from which his narrations were written. This methodology is called "selection from the narrations of the weak," meaning that a weak narrator's hadith is neither rejected entirely nor accepted entirely; rather, only what is sound from it is accepted. Similarly, the narrations of a trustworthy narrator are not accepted absolutely; rather, what he narrated correctly is accepted, and what he erred in is rejected.

Scholars differed on accepting the narration of a liar in hadith who has repented. The majority do not accept it, while Al-Nawawi holds that it is accepted if his repentance is sincere. An example of this is Isma'il ibn Abi Uwais, who was accused of lying. However, Al-Hafiz Ibn Hajar believes that he repented, and that what the Two Shaykhs narrated from him is part of the sound (sahih) narrations in which trustworthy narrators also participated. Al-Hafiz Ibn Hajar summarized Isma'il's condition as being "truthful, but he erred in some narrations from his memory." Isma'il was one of Al-Bukhari's teachers, and Al-Bukhari narrated from his original sources after Isma'il permitted him to do so. This indicates that what Al-Bukhari narrated from him is from his sound hadith. As for 'Uthman ibn Abi Shaybah, he was considered trustworthy by Ahmad and Yahya, but he did not memorize the Quran and might make mistakes, yet the Two Shaykhs relied on his hadith.

For more detail, it is recommended to refer to Al-Hafiz Ibn Hajar's introduction to the commentary on Sahih Al-Bukhari (Hady Al-Sari), specifically chapter nine.