A water distiller wouldn't run a filter at all. It's a distiller which by definition means it utilises the process of distillation to filter your water - heating it to boiling point and collecting the distillate.
I don't think many people actually have distillation systems in their homes...
Alasdair, the small home water distillers about the size of a kettle use at least one filter to trap VOCs. The better distillers use two filters. A large size glass / pyrex distiller that you might see in a chem lab has a much longer column and does not need filters.
Frank, not the right time to do more plumbing to my house. We are AC 'friends' so send me more info if you like.
He's also a naturopath. This should result in you taking anything he tells you with a grain (or possibly shaker) of salt!
Don't buy any filtration system which de-flouridates or to any major extent de-mineralises your water.
I saw a quack naturopath that put me off them for years. This naturopath takes small sample / drops of blood which he then magnifies to describe the cells and his client's health. Can tell if not enough of some cell types, too much of another, and if some cell types are under stress. Think of chemistry classes where different chemicals have different shapes and/or colours. His comments supported many of the things I knew from my doctor and regular blood tests.
I accept the studies of some that extra fluoride in the water is unhealthy (there is some in the foods we eat). In earlier housing I survived drinking rain water by brushing my teeth.
A common myth that one hydrates only with water. Get water from milk, even from coffee, and from food. Obviously more fluid in a fruit salad than biscuits.
Clayton, was your first sentence tongue-in-cheek? Coffee can act as a diuretic but for people who are accustomed to drinking it, no obvious running to the toilet and does provide some liquid.
They are but the literature seems to show that you can rehydrate even with a diuretic.