The mathematical part of quantum mechanics is a tool to analyze the physical world. Statistical probability works in ordinary situations as well. But explaining it as the physical nature of things is what I object to. I think the electron is indeed a particle, and not a wave. The term tunneling is used to show that the electron crosses a barrier, and the probability for it can be mathematically calculated. They say that they have photographed an electron. Though it is done indirectly, I think it may go against uncertainty principle (I am not sure).