In Islam, it may be difficult to say which has higher authority between the Qur’an and Muhammad. However, the Qur’an and its supporting document clarifies this.
Asbab ul-Nuzul is the document that explains the background contexts for different verses. Here is the one for Qur’an 2:62.
Salman Al Farsi used to be a Zoroastrian, but then spent a number of years as a Christian, before finally becoming a Muslim. He asked Muhammad about the fate of those righteous Christians he knew. Muhammad´s answer was that they all will be in Hellfire. Naturally Salman Al Farsi was disappointed. Then a new revelation was given to Muhammad, correcting the prophet.
Q. 2:62 says, “Those who believe in Islam and those who are Jewish, Christian, or Sabean, anyone who has faith in God and the last day and who does what’s morally right, their reward will be with their Lord, and they’ll have nothing to fear or regret.” (Emerick translation)
This clearly indicates that the Qur’an has higher authority over Muhammad.
In addition, during the life time of Muhammad, he told his followers that the Qur’an has higher authority over what he says. His followers wanted to mix the Qur’an and what he said. But he told them to differentiate the two clearly. That is why they have a separate document called “Hadith” (the sayings of Muhammad).
This short discussion clearly shows that the Qur’an is the highest authority, not Muhammad. What is the conclusion? If a proper interpretation of the Qur’anic text shows that Hadith or Shariah is not consistent with the Qur’anic text, then Hadith or Shariah should be corrected to make it consistent with the Qur’an.
Actually many Muslims are talking about “Islamic Reformation.” Following the text of the Qur’an and having the correct interpretation using proper contexts for the verses of the Qur’an is one way to change the traditional Islamic practices and interpretation. This was exactly Martin Lurther did to Catholicism and started Protestant movement.