I think that, when he says that "The Theory of Evolution and The Theory of the Big Bang do not need to be proven," he means that there are already enough evidences to believe that those scientific theories are accurate. For example, the theory of evolution is the most plausible description of the mechanism because it perfectly describes the observed reality. In that sense, it does not need to be proven since it's the most likely explanation (assuming Occam's Razor).
A theory can be called into question if new evidences show behavior that cannot be explained by the current model, but a scientific theory does not need to be proven since it is, by definition, the most plausible explanation.
For as long as it explains the mechanism perfectly, scientists assume it is correct.