Had this tradition been authentic...
Had this tradition been authentic, Abu Bakr would have first cited it, and then Umar, in order to justify their prohibition of recording hadith, and they would have erased them, and those who had recorded them would have sought an excuse for having done so either due to their ignorance [of such a "tradition"] or to their lapse of memory. Had this tradition been authentic, Abu Bakr and Umar would have had to erase all traditions, not burn them.
Had this "tradition" been authentic, the Muslims, who were contemporary to Umar ibn Abd al-Aziz, till our time, would have been committing the sin of disobeying the Messenger of Allah, particularly their chief, namely Umar ibn Abd al-Aziz who had ordered the scholars of his time to record hadith, in addition to al-Bukhari and Muslim who regarded this tradition as authentic yet they did not act upon it but wrote thousands of the Prophet's ahadith.
Finally, had this "tradition" been authentic, it would not have been missed by the gate of knowledge Ali ibn Abu Talib who compiled the ahadith of the Prophet in one saheefa the length of whose pieces reached seventy yards which he called al-jami`a, the one that includes everything, and which we will discuss later by the help of Allah.
SECOND: Umayyad rulers spared no efforts to underscore their theory that the Messenger of Allah was not protected by Allah against falling into error as is the case with all other human beings who sometimes are right and sometimes are wrong, fabricating several "traditions" to support their claim.
The purpose of fabricating such "traditions" was to make sure that the Prophet used to follow his own personal views; therefore, he often erred to the extent that some of his companions had to correct him, as indicated in the incidents of palm tree pollination, the revelation of the verse referring to the issue of hijab (veil), the case of accepting fidya (ransom) from the captives seized after the Battle of Badr, in addition to many such incidents claimed by "Ahl al-Sunnah wal Jama`ah" and included in their Sahih books in support of such an attitude towards the Messenger of Allah, peace and the best of blessings be upon him and his progeny.