Here is Jim's reply I was actually referring to anything like distilled or triple distilled or produced from your own still. I'm most addressing. Distilled vs DI supermarket bottled water is just not that big a difference to worry over.
Reverse osmosis is just fine.
I'm not too concerned about stripping out protective cations. One added word of caution from a Californian. Viruses still seem to be able to get past them. Culligan may be saying that to save themselves from litigation because I picked up a virus-filtering system at a local camping outfitter for 60 bucks which doesn't seem any higher technology than the DI system I purchased. I bet Culligan is really saying that it's hardware installations across the board will have ways viruses can get around them rather than the filters aren't good for such small submicron particles.