I believe he is referring to pinch flats. Stuffing the larger tube stands a chance of the tube getting pinched between the tire and rim.

That being said, I have 32 tubes inside my 25 tires but I'm always very careful to avoid pinching the tubes in the bead seat and haven't had a pinch flat since I learned to mount my own tires as a kid. And at my age, that is a long time.