Assalam alaikum
Shia say" if Hafs isn't trusted to transmit Hadeeth, how do you trust him to transmit Quran ?
Al-Bukhari: “They (scholars) rejected him”
Muslim: “Rejected”
Al-Nisai: “Rejected” and “Not reliable, and his narrations are not written”
Ibn Hanbal, as reported by Ibn Abi Hatim through Abdullah: “His narrations are rejected”
Ibn Hanbal, as reported by Al-Dhahabi: “Yahya Al-Qattan narrated to me: Shu’bah mentioned Hafs ibn Sulayman and said that he used to take people’s books and eradicated them, he took his books and never returned it.”
Ibn Mu’in: “Not reliable” and, as related by Al-Saji, “Hafs and Abu Bakr (ibn Ayyash) were the most knowledgeable of people on the qira’ah of Asim, and Hafs’ recitation was better than Abu Bakr’s, but he was a liar and Abu Bakr was truthful”
Al-Darqutni: “Weak”
Ibn Hajr: “His hadeeth are rejected, despite that he is a leader in qira’ah”
Abu Hatim: “Rejected, he was not truthful”
Ibn Kharash: “Liar, fabricated hadeeth”
Ibn Uday: “Generally his ahadeeth are not protected”
Ibn Hibban: “He changed the chains of transmission, and fabricated chains for those that were mursal, and he used to take people’s books and eradicated them, and narrated them without having heard them.”
Ibn Al-Madini: “His hadeeth are weak”
Salih ibn Mohammad: “His hadeeth are not written, and all his hadeeth are objectionable”
Al-Saji: “He narrated from Sammak and others unfounded hadeeth”
Abu Zar’ah: “His hadeeth are weak”
I searched this site for answer but didn't find any.
Jazakum Allahu khaira
The key word here is
MUTAWATIR. When a report
has proven to be mutatawir i.e. the report is so wide spread that it reached to a level where it is impossible for people to lie about it, the need for sanad to be scruntized will not be there anymore. You might find a hadith in a book that contained a very week narrator (or even a fabricator) in its sanad but since you know the hadith is MUTAWATIR, you can still relay the hadith to other people without to worry about prophet's warning of people lying on his name.
No recitations will be called Al-Quran if they are not MUTAWATIR (some khilaf about shadz readings though). Regardless the conditions of Hafs, the recitation itself is mutawatir. The recitation was so widespread during his time and even generations before him. Nobody, during his time, would accussed Hafs of making a lot mistakes in his recitations since they can easily check with lots of other people.
But why Hafs among all people? Because a qira'at are named after the leader of a school of Qur'an reciters. Each qira'a derives its authority from a prominent leader of a particular recitation. And Hafs was a prominent student of one of the qiraat leader i.e. Asim.