There are some separate questions in regards to your question:
First whether or not there are evidences from Quran, Hadith (or reason in case the latter is an accepted criteria and to which extend which depends on one's jurisprudential position) as to why a hadith coming or narrated by a fallible companion (unless belonging to the circle of the Infallible Successors of the Prophet, a doctrine not shared by all muslim sects) that is in clear, irreconcilable conflict with definite teachings of Quran should not be heeded.
Second, whether the edit was valid.
The sectarian more theological aspects of the first question would obviously affect the views of the sects in regards with their version of ilm-ul-hadith. While both prominent sects believe in existence of fabricated hadiths (and hence the importance of various authentication methods), Shias put much more emphasis on the principle of non-contradiction with Quran for at least the followings reasons (as far as I know): 1) that they can a) demonstrate their distinct beliefs by Quran, b) likewise to refute rival sectarian beliefs using Quran; 2) Shias believe in a much higher extent and more crucial instances of hadith fabrication than do the Sunnis (hence the importance of more strict authentication criteria). 3) Shia don't consider all companions to be righteous (much less to be infallible) to treat their words as of equal status with Quran. So it is crucial for them to verify the source (infallible or not ), transmission (sound, honest, accurate or not) and the content (consistent with definite teachings of Islam) of a hadith as to be valid according to Quranic doctrines.
However while the emphasis on non-contradiction seems to have more significance to and more strictly applied by Shias (the contrary being true for Sunnis schools as evidenced by the Wiki page you linked which clearly reflects the Sunni perspective), yet the Sunni schools can't also deny the validity and importance of such a principle for their shared belief in supreme authority of the Holy Quran, for Quran is believed by all muslims to be infallible words of Allah revealed to the Holy Apostle and preserved authentically thereafter. This alone elevates Holy Quran to the level of highest ultimate authority over any words of fallible men. So the very status of Quran as agreed by all sects, is sufficient to demonstrate why a hadith that could be affected by various fallible factors — the author when not being the Prophet himself or any other infallible with unquestionable authority; the narrators who may compromise faithful transmission of the hadith for various reasons; or the outright hadith forgers known to have existed by all muslim sects — and is in clear conflict with the Quran has to be dismissed.
This view is also further confirmed by an answer by a Sunni/Salafi user to exactly this very question.
For these reasons this principle should be considered vital in hadith verification but the answer failed to address such an important criteria. However if such negligence or failure of significance, as I said, is due to particular scholarly views among Sunni schools of jurisprudence, then the answer has to specifically mention that it is giving the Sunni view, for the question doesn't specify which school he expects answers from. Otherwise, with the explanation I provided above, the addition of the sixth principle helps (although just a little) towards an answer that reflects a more comprehensive view held by muslim schools.