I've sent an email to the DMT asking for citations. I'll let you know if he produces any.
In reply to flots, I just picked the first link I came to that had an easily quotable summary, and it happened to be the Water Benefits one. I'm not buying into anything, just exploring viewpoints. It's nothing more than a fairly typical example of what I saw in online claims.
In RE distillation, there is a lot of distillation here on my island. We don't have any rivers, and many wells are brackish (I don't have a well, for example, I have to pipe in water, because at the water table the water is brackish). What water we do have here is rain runoff that collects in the old tin mining ponds during the monsoon season. We have water issues here, and there is a fair amount of distillation for locally bottled water.
I personally dislike electrolyte drinks of all types, whether they're prepared ones, homemade ones, or ones created by pouring powder into a bottle of water. Yuck. If I had to rely on those for rehydration rather than water, I'm sure I'd drink far less fluid.
Now for bottled water marketed throughout the Kingdom, there are sources for some (up in the northern highlands where Minéré, a Nestle product, is bottled), and some, like the one I buy, undergoes a different process--the label on the water I usually buy says it's ionized and filtered, for example. But the DMT pointed at my water and said very clearly that it was one of the less desirable ones, that the body does get some degree of hydration from that water, but not as much as with mineral water like Minéré. I figured there would be people in the know here who could either debunk or support this guy's statements.