Do certain cameras or ways of working confer a cloak of invisibility on the user ? Perhaps they are more discrete or less obtrusive ? I had great fun shooting street shots today with a black M6 and 28mm Elmarit and I really felt un-noticed. I know that Henri Cartier Bresson was renowned for his stealth. Does confidence help here ? I guess it helps if you are noticed but look like you have a right to be there and aren't appearing furtive.
I don't think there is any magical cloak of invisibility. No camera can give you that.
Cameras such as the Leica M, Leica CL, Rollei 35, Minox or Olympus Trip 35, Nikon S series and Bessa rangefinders are small and for some reason less "threatening" or intimidating to others. I can't quite grasp why that is, but it seems to be the case. So for street photography, smaller - and quieter - is better.
The way you work is very important. If you project an attitude of relaxed professionalism people around you are put at ease. They assume you are not anyone to worry about and take it for granted that what you are doing is legitimate. If a street photographer is nervous or jumpy, he/she will make others nervous or jumpy.
When you make your photograph is important too - the timing of the shot is everything. I have had many instances where people notice me with my camera and then go about their business. It is this point in time when they have stopped watching you that is the time to make your photograph. They have returned to their world and have let their guard down, so to speak. This is when you can capture the decisive moment that Henri Cartier-Bresson spoke of.
Some people will just not stop watching you, though. They will continue to shoot furtive glances your way or watch you out of the corner of their eye. When that happens, I simply give up on them and find another subject. A photograph of a rigid, tense subject who is watching the camera with an accusatory expression is not a good street photograph anyway. It's just a waste of time and film (or memory card space) in my experience. Photos of wary people almost never turn out to be good images.
These are my thoughts and experiences regarding street photography.
Hope this helps...