The idea is that karma doesn't doom us to relive things just as they happened before. It makes us relive those moments in which we made a "wrong" choice, or a choice we're bound to by regret or sadness, or habit, or pleasure, and presents itself until we make a choice that frees us from this bondage.
This is definitely a modern concept of karma, and definitely not one I'd mark as "authentic," but it is very thought-provoking. It also raises a good point in that karma is not meant to be so concrete. It's not something that forces us to undergo the reciprocity of an action we previously made. And, it's something we bind ourselves to. It's more like a bias, really.
Let's take some simple: every guy named Larry you've ever met was a jerk. The next time you meet a Larry, you could assume that he's a jerk. Or, you could take a page from David Hume and take this is a separate, unrelated event, and take it as is.
If any of you have ever played Enter the Matrix, you may recall a scene between Niobe and Ghost. The weapons program loads up, they choose their weapons, and Ghost checks the cartridges in his guns. Niobe mentions that the program loads the same way each and every time, yet Ghost never fails to check his guns manually. She asks him why. In response, he says,
Hume teaches us that no matter how many times you drop a stone and it falls to the floor, you never know what'll happen the next time you drop it. It might fall to the floor, but then again it might float to the ceiling. Past experience never proves the future. (source)
Not a bad way to approach things, I might add. Going about things this way allows you to approach things from a fresh perspective each time. While it's quite an exercise, it forces you to shed biases and often makes it easier to peel apart layers from things when you're feeling very overwhelmed.
Bias is very useful. If we touch a hot stove, we get burned. We learn not to do it again. However, things aren't so black and white in every case. I don't think I need to point out how irrational it is to assume the next Larry you meet is going to be a jerk. But, that is how our brains work, sometimes even if it happens sub-/un-consciously.
karma can work in a similar way. If we're faced with one situation over and over, we can very easily take a pitfall and assume things will unfold the same way. We often have to work to realize that we can actively make a different choice, or influence the event in different way.
There's also another choice, one that's "neutral." We can let go. Instead of waiting for a karmic credit card bill or tossing something into our karmic bank accounts, we can choose to just let go. We can accept something as is, react without emotional attachment, and move on. Notice that I said "without emotional attachment," and NOT "without emotion." There's a large difference here that amounts to more than one word. If we bind ourselves to things and have to unbind ourselves from them later, we can also choose to not be bound in the first place.
Personally, I feel that part of life is having these bound experiences, and part of it is learned to act without having to bind yourself. Your mileage may vary, of course.
In nearly all of the various schools on Indic philosophy, orthodox and heterodox, you see that people who have attained their respective goals do no produce karma. That is not to say that there is absolutely no interaction with karma, as they can just be spouting out a balance of zero. I think I previously mentioned that it does not necessarily imply causation, either; by tweaking your karmic output to zero you may not find "liberation," or "enlightenment" or what have you. But, that doesn't mean you can't improve your life.