@Tru, I found the interpretation I was thinking of. There's this book, Engaging the Powers: Discernment and Resistance in a World of Domination by Walter Wink. In it he interprets this part of the sermon as ways to non-violently subvert the power structure of the time.
As I said originally, striking someone deemed to be of a lower class with the back of the hand was used to assert authority and dominance. By turning the other cheek, the assaulter faced a dilemma; a forehanded slap was viewed as a challenge which would imply equality between the two, the left hand was used for 'unclean' purposes so preforming a backhanded slap with this hand would be to admit the act as unclean, and to do nothing showed weakness or lack of authority.
When someone sued you for your shirt/tunic, giving them your cloak as well would leave you naked, not only was this a situation forbidden by Hebrew law according to Deuteronomy, but based on Noah in Genesis, public nudity brought shame on any viewers present, not just the naked.
The going an extra mile part is also interesting because at the time, the occupying Roman troops could command a citizen to carry their things for one mile, no more. If it was found out that an individual had exceeded this distance, the soldier who had demanded their help risked suffering disciplinary actions.
So really the message wasn't to just be passive and compliant to injustices, but rather act in a way that discouraged them from being preformed in the first place while still maintaining a nonviolent approach.