I've been reading the Qur'an for over 20 years and have not encountered this particular tenet. Could you please give me verse numbers?
(Btw, for future reference, when a person says, "Islam teaches ....", he should always provide the source verses. Otherwise, a person could say anything fantastic thing about islam. I once heard a woman claim that the Qur'an gives women the vote.
Referring hadiths to Quran is important. But sometimes, a person has not passed primary teachings. However, I would look at two places. Surah Noor where believers are advised not think of other believers in a bad way. And the other in Surah Ahzab, which it's important to never say about believers evil things they didn't commit.
You can infer if you can't prove something, not to speak about it. And even it is proven, backbiting is forbidden.
This leaves "thoughts in our mind", and so we can derive, that if there is 70+ excuses we can make up, we should, because for all we know, this excuse is there. If we assume otherwise, we are accusing believers possibly of something they did not commit.
Thus this hadith can be inferred to be verified in Quran. But I will provide further evidence in Quran from the hadith found in Misbahal Shariah, Imam Jaffar (a) says:
The root of good opinion is a man's belief and the soundness of his heart; the sign of good opinion is that whenever he looks, he sees with the eye of purity and virtue wherever he goes, and modesty, trustworthiness, protection and truthfulness are cast into his heart. The Holy Prophet said, 'Have a good opinion of your brothers: through that you will gain purity of heart and firmness of nature.' And Ubayy ibn Ka'b said, 'When you see a quality which you disapprove of in one of your brothers, then give it seventy interpretations and see if your heart can be at peace with one of them. If it is not, then blame yourself if you cannot excuse him. If you yourself have a quality which will easily make for seventy interpretations, then you should disapprove of yourself more than you do of him.' As Allah revealed to David, 'Remind My slaves of My blessings and My favours. They have only seen exquisite goodness from Me so they should only expect that what remains will be like what they have already had from Me.' Good opinion invites good worship. A person who is deluded continues to remain in rebellion even while he hopes for forgiveness. The best opinion in Allah's creation is reserved for those who obey Him, hope for His reward and fear His punishment.
The Messenger of Allah said, relating from his Lord, 'I am with My slave's good opinion of Me, O Muhammad.' Whoever fails to live up to the reality of the gifts which come from his opinion of his Lord has intensified the proof against himself, and is among those who are deceived by the shackles of his passion.
We can see Imam Jaffar (A) linked having good opinion about God with good opinion about believers.
This can be derived from the link of "great" "exalted" and "God" in Quran. The exalted ones are not God, but they are exalted due to their relationship to God and proximity to him, and exalted are great, but believers are not exalted but they are great. Exalted is for God's chosen elite sent ones to humanity and chosen close Angels to him.
Exalted has it's own sacred ground, you can't "go beyond it" or you equate chosen ones with Godhood and belittle God's station by equating others with him, but it also has a sacred territory that others should not be raised to their position and status and role in this world.
That said, the addition in "atheem" even though God is Exalted, and if you are exalted, you are great, and the wisdom of bowing in prayer, is to respect believers and their greatness linked to God's greatness and the greatness of his exalted ones. They have a right to be honored.
Now with God, there is many trials in life, and a world in chaos and many trials with this world, but believers still maintain a good opinion and seek an explanation from God for why the word is as is in it's evil and chaotic state.
Now with Messengers and chosen ones, they have overwhelming power, but we see they don't fully use it, but only by God's permission, and someone can assume if they are killed, they are sorcerers, for if they were God's chosen, they would not be killed. They can measure their honor by kingdom worldly sense. But believers exalt them, know their power will be only manifested fully on day of judgment and their light will be manifested then truly, but despite the ordeals and afflictions they face, and their followers face, they assume the best of them and they are truly exalted and beyond our appreciation.
Believers although less then exalted, still are great, and God tries them to bring the best out of them. Some he allows to fall in ignorance only to turn back to him sincerely. Some he tries with vast insights but not much power, but if they pray to him with knowledge, he will give them power. And so believers are tried differently, but same principle of assuming best applies to them.
