A good distiller does remove VOCs actually. In terms of pH, I'm not 100% convinced either way. There's also the issue of pH metabolism in the body which is ultimately more important.
This argument is much like fruit. People use citrus for cleaning agents, but without question it has an alkaline effect inside the body. There's much misinformation out there about fruit being acidic to the body. My bet is distilled water has similar ignorance.