Well, the old saying that some pictures can only be taken with a Leica rangefinder camera is bullshit.
What is true is that it's unlikely you'll catch a candid moment with a big fat DSLR because these kits are so big you probably don't bring them wherever you go. That gives you plenty of "I wish I had my camera with me" moments. With a Leica M, not so much.
Also, the rangefinder is built in a way that you can take photos very (and I mean VERY) quickly. Don't listen to people who tell you that you should use zone focusing, you don't need a rangefinder to do that. I mean real sharp focus right on point. With experience, you instinctively know where your finger should go to focus at a certain distance.
A Leica camera is the perfect tool to snap pictures very very quickly while keeping complete control over the process. So, there is no such thing as "pictures you can only take with a Leica rangefinder", but good luck getting the shot quicker than a Leica guy with years of training.