It is really amazing, and they even discuss it in the podcast. What the interviewee basically says is that quantum mechanics is the reality of how things work, and that classical physics, including general relativity, is an approximation of how QM works in large scales. In the end he says one day we may be able to think of an experiment to measure the things the theories don't agree upon. He guesses this may come from experiments around Lorentz invariance.