The Essence of Avraham's Hospitality

"Hashem appeared to him in the Plains of Mamre while he was sitting at the entrance of the tent…" (18:1)

Rashi explains that Avraham was sitting at the entrance of the tent “to see if there were any passersby (Over Vushuv) so he could bring them to his house.” 

How does Rashi know this? His source for this teaching is the Talmud (Bava Metzia 86b). 
However, there is one striking contrast between Rashi’s words and the Gemara he purportedly quotes. The Talmud uses the word Orchim (guests) to describe the individuals Avraham was seeking to bring to his house, but Rashi describes them with the term Over Vushuv (passersby). 
Why does Rashi depart from the precise wording of the Gemara? 

 I once heard an interesting answer that proceeds as follows: 

The word “Over” is similar to the word aveira (sin), and “Shuv is cognate with the word Teshuva (repentance). 
These words hint to the idea that Avraham wasn’t interested in merely welcoming people into his tent and feeding them, but his primary interest was helping them in the spiritual domain. 
While always a gracious host, Avraham was most interested in hospitality directed towards the Over (ie. the individual who sinned) and helping them Shuv (ie. do Teshuva and return to Hashem)! 
Rashi chose this expression instead of the word in the Gemara to help emphasize and encapsulate the essence of Avraham’s hospitality.
Rabbi Shlomo Zalman Bregman is an internationally recognized Torah scholar, #1 best-selling author, matchmaker, entrepreneur, attorney, and media personality. His energetic and empowering messages currently reach over 350,000 people per week via social media, NYC radio, and newspaper columns worldwide. His website is www.RabbiBregman.com and his email is RabbiBregmanOfficial@gmail.com.