Here is my current thoughts in response to your questions. I want to first of all praise your concerns, it’s good not to ever jump on the bandwagon, or adopt a philosophy without giving in more consideration.
The verses you mentioned regarding governing authorities also are valid and worth considering. Romans 13 comes after Romans 12 which says,

17Do not repay anyone evil for evil. Be careful to do what is right in the eyes of everybody. 18If it is possible, as far as it depends on you, live at peace with everyone. 19Do not take revenge, my friends, but leave room for God’s wrath, for it is written: “It is mine to avenge; I will repay,”[d]says the Lord. 20On the contrary:
“If your enemy is hungry, feed him;
if he is thirsty, give him something to drink.
In doing this, you will heap burning coals on his head.”[e] 21Do not be overcome by evil, but overcome evil with good.

It would seem to me that that would point toward a justice oriented mindset, but one that does not encourage or perpetuate violence, nor it seems, press charges.

In addition, Jesus’ example of what he meant by ‘love your enemies’ seems to indicate also that we live out a radical example of love that doesn’t rely on the kingdoms of the world, but rather the Kingdom of God.

I know this is a short response, so feel free to ask more questions. I’ve written on the topic before, but it would be good to have a fresh dialog on things now.

http://www.npr.org/templates/story/story.php?storyId=89164759&ft=1&f=1021

It doesn’t say if Julio is a Christian or not, but I’d have to say he is if he offered the coat off his back. Thats such a Jesus like thing to do. I’d love to hear if theres a Christian version instead of the more secular version that NPR offers. If not, thats ok, He is Christ-like either way.

I know that the bible said its God’s kindness that draws us near, and its amazing to see how disarmed the mugger was when presented with such a kind act.

Also, it is so very sermon-on-the-mount-esque it’s amazing.

http://www.npr.org/templates/story/story.php?storyId=18791726

I am intrigued by the non-violence “movement” if you will. While it appeals to me and affirms erroring on the side of grace, I also have some red flags that popped up when I read your post. While I am moved by Julio’s care for the man who robbed him, and can assume the result on the young man’s life, I also think that an incident such as that could be taken out of context and used to allow criminals to “get away” with their crimes. On this level, the story of Julio can be prized by advocates of non-violence. Yet, what about justice? God elevates justice as well as grace. We are not the ultimate judge, but God has put people in authority in government and provided laws to follow. No matter how flawed we are as humans, no matter how flawed we are in government, God has still told us to follow the the governing authorities (Rom. 13:1-3). I understand having issues with our current governing administration. But didn’t God institute the method of having governing authorities? In other words, that man broke the law. It’s incredible that Julio offered that man his coat, and I am so thankful that God allows our hearts as Christians to do things contrary to how the world would have us operate (and if more people acted in response to the Spirit, then maybe our government could look different?), but is that to say that he should not report the incident? Somehow grace and justice have to go together. And as reflections of God here on earth, how do we do that? I apologize that this is not very well articulated. I’m queen of “half thoughts” and verbally processing things. . .