I'm at a point where I am tired of the black and white view of things; which usually ends with people just trying to live their lives being told, not to let go, but to GIVE UP.
I like what you described as the Native American view, not so much the Christianized version.
Here is the first definition I found listed for "forgiveness":
Forgiveness is the renunciation or cessation of resentment, indignation or anger as a result of a perceived offense, disagreement, or mistake, or CEASING TO DEMAND PUNISHMENT OR RESTITUTION.
The caps are my emphasis. I fully believe in people being treated justly, but if "forgiveness" is to cease to demand restitution for a terrible wrong of some kind, that's not justice and I believe it is demeaning to those who do not do great harm. I believe that one can detach emotionally enough so that the flames of hatred are not burning you up from the inside (that's self abuse IMO) and still work toward a more just society. This is just what I have come to in my life, subject to change but I don't see where I am as defective because I have an alternate view of the word "forgiveness".
Edit to add: My IDEAL (not doable by me really, since I become insensed over horrific injustices to the innocent and am working on detaching there) would be to not be eaten alive by rage against people who abuse animals or children, but still call for justice to be done, real justice, so to make these crimes less common in our society. Justice is to work toward ending that person's damaging behavior, take the pedophile off the streets, create tougher laws that take animal abusers off the streets for greater lengths of time, laws that require real counseling and follow-up. Right now I do get too eaten up over these issues, but I'm working on more emotional balance, but I still think justice needs to be served.