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 is His slave and Messenger.
First of all, we ask Allaah to reward that sister for being keen on learning and studying the Quran, and may Allaah reward you for avoiding to speak about religious matters without knowledge.
As regards the expression that is mentioned in the question, its meaning is correct because it means justice and equity when dealing with people. There is evidence in the Quran about this, like the verses which order to be just, such as the saying of Allaah (which means): {O you who have believed, be persistently standing firm in justice, witnesses for Allaah.}[Quran 4:135]
Moreover, this meaning is explicitly mentioned in the Sunnah. The Prophet said: “Whoever wants to be drawn away from the Fire and admitted to Paradise, let him die while believing in Allaah and the Last Day, and do for the people what he likes them to do for him.” [Muslim]
Moreover, Al-Bukhari reported a statement from ‘Ammaar ibn Yasir which reads: “There are three characteristic if one has them, he has gathered the characteristics of faith, and he mentioned amongst them ‘to take others’ rights from oneself’; this means to deal with people in the same way you want to be dealt with, as stated by the scholars .
It should be mentioned that Islam is a religion which advocates good moral conducts and good traits, but this does not necessarily mean that every detail about that is proven with specific evidence in the Quran; as it might be proven in the Sunnah, because the Sunnah is evidence in the same way the Quran is evidence.
Finally, it should be mentioned that a man should observe Islamic pre-conditions when dealing with a non-Mahram woman in order to avoid the means of temptation.
Allaah Knows best.