There have been many, many published demonstrations of the effect of the reflex mirror. They confirm my own tests, which show that it does indeed cause vibration that is visible in the image... in certain circumstances. Like most things, sometimes it matters and sometimes it doesn't. Also, putting the camera on a tripod doesn't necessarily help. A light tripod will often damp the vibration less than just holding the camera in your hand.

That said, I'm back to shooting with an SLR about 80% of the time after a few years of being rangefinder-oriented, because of other advantages.