That translation would seem to move us simply to doing good to those who the culture defines as least. But there is more. I was a stranger and you welcomed me. I was a stranger and you brought me together with Yourselves and welcomed and entertained and lodged me. So much for the we let you in but don't expect anything else inherent in the least of these mentality.
Lets go back to the start of the story.
Jesus first welcomes those who have done the feeding and clothing and welcoming and visiting. They were surprised. Jesus says to them when you saw me hungry, you fed me, and they answer, we never saw you hungry. They must have seen John hungry, or Margaret, or Linda, or Sam, and provided food for they dearly fed somebody. The implication is that in the context of their lives, the hungry person had not only a need but a name and worth and dignity, and that there was not an us-them relationship but rather one in which Jesus himself along with his friends the hookers and the thieves would have been welcome.