All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
First of all, you should bear in mind that Abu Hurayrah would have never changed the reported words of the Prophet, sallallaahu ‘alayhi wa sallam; all the honorable Companions are trustworthy and would have never made a lie about the Prophet, sallallaahu ‘alayhi wa sallam, or falsely attributed fabricated words to him. Qataadah narrated that a man asked him, “Have you narrated such and such Hadeeth on the authority of Anas?” Qataadah replied, “Yes, I have; and a man asked Anas, ‘Did you hear such and such Hadeeth from the Messenger of Allaah, sallallaahu ‘alayhi wa sallam?’ Anas said, ‘Yes,’ or he said, ‘I heard it from some person who never tells a lie. By Allaah, we never lied and we did not know what lying is.’” [Al-Bazzaar]
‘Umar himself appointed Abu Hurayrah both, as a governor and this proves that ‘Umar trusted him. Please, refer to Fatwa 89722 underlining the virtues and merits of Abu Hurayrah and the reson for the blessing of reporting the greatest number of Ahaadeeth bestowed upon him by Allaah.
The reported traditions regarding ‘Umar forbidding Abu Hurayrah from narrating (the Hadeeth) was not because he - we mean ‘Umar - questioned Abu Hurayrah’s trustworthiness or accused him of lying. In fact, ‘Umar forbade others as well from (writing down or even) reporting the Hadeeth in general - as cited by Ibn Katheer in Al-Bidaayah wa An-Nihaayah and others. This was because ‘Umar did not wish to preoccupy Muslims with narrating (or writing) the Ahaadeeth instead of paying their undivided attention to the Quran. When he sent Abu Moosa to be governor of Iraq, he advised him, “I am sending you to a people who recite the Quran in their Masjids like the buzzing of bees; so leave things as they are and do not preoccupy the people with (reporting) Ahaadeeth.”
‘Umar also forbade Muslims from quoting the sayings of the Prophet, sallallaahu ‘alayhi wa sallam, (in speech or in writing) too much fearing that people might misunderstand the Ahaadeeth (out of their proper religious context) or indulge in exploiting the religious concessions understood from them. Moreover, there is a possibility of committing mistakes on part of the narrator while reporting so many Ahaadeeth. Ibn Katheer wrote, “The actions of ‘Umar in this regard are interpreted to indicate his fear that people might misunderstand or misinterpret the Ahaadeeth or may exploit the religious concessions in the Ahaadeeth. Moreover, a narrator may commit mistakes unintentionally in reporting the Hadeeth and people might mistakenly assume that that was the exact wording of the Prophet, sallallaahu ‘alayhi wa sallam, or the like. It is reported that ‘Umar later on gave permission to report (and write down) the Hadeeth.” [Al-Bidaayah wa An-Nihaayah]
Allaah Knows best.