I stand corrected and I realize the error in my posting.
Let me see if I can demonstrate what I really do mean, I do realize the distilled water does not have all the good stuff, though several things can carry over with distilled water, thats a different discussion.
R/O vs Distilled
Typical home water softeners soften water using a technique known as "ion exchange". That is, they remove calcium and magnesium ions by replacing them with sodium ions. Although this does technically make water softer, most fish won't notice the difference. That is, fish that prefer soft water don't like sodium either, and for them such water softeners don't help at all. Thus, home water softeners are not an appropriate way to soften water for aquarium use.
I guess the true reason people use R/O water or Distilled water is to affect pH. So, lets define pH.
pH refers to water being either an acid, base, or neither (neutral). A pH of 7 is said to be neutral, a pH below 7 is "acidic" and a pH above 7 is "basic" or "alkaline". Like the Richter scale used to measure earthquakes, the pH scale is logarithmic. A pH of 5.5 is 10 times more acidic than water at a pH of 6.5. Thus, changing the pH by a small amount (suddenly) is more of a chemical change (and more stressful to fish!) than might first appear.
To a fishkeeper, two aspects of pH are important. First, rapid changes in pH are stressful to fish and should be avoided. Changing the pH by more than .3 units per day is known to stress fish. Thus, you want the pH of your tank to remain constant and stable over the long haul. Second, fish have adapted to thrive in a (sometimes narrow) pH range. You want to be sure that your tank's pH matches the specific requirements of the fish you are keeping.
Most fish can adjust to a pH somewhat outside of their optimal range. If your water's pH is naturally within the range of 6.5 to 7.5, you will be able to keep most species of fish without any problems. If your pH lies within this range, there is probably no need to adjust it upward or downward.
With this now know we need to address the Buffering Capacity. (true problem with distilled and R/O)
Buffering capacity refers to water's ability to keep the pH stable as acids or bases are added. pH and buffering capacity are intertwined with one another; although one might think that adding equal volumes of an acid and neutral water would result in a pH halfway in between, this rarely happens in practice. If the water has sufficient buffering capacity, the buffering capacity can absorb and neutralize the added acid without significantly changing the pH. Conceptually, a buffer acts somewhat like a large sponge. As more acid is added, the "sponge" absorbs the acid without changing the pH much. The "sponge's" capacity is limited however; once the buffering capacity is used up, the pH changes more rapidly as acids are added.
Buffering has both positive and negative consequences. On the plus side, the nitrogen cycle produces nitric acid (nitrate). Without buffering, your tank's pH would drop over time (a bad thing). With sufficient buffering, the pH stays stable (a good thing). On the negative side, hard tap water often almost always has a large buffering capacity. If the pH of the water is too high for your fish, the buffering capacity makes it difficult to lower the pH to a more appropriate value. Naive attempts to change the pH of water usually fail because buffering effects are ignored.
In freshwater aquariums, most of water's buffering capacity is due to carbonates and bicarbonates. Thus, the terms "carbonate hardness" (KH), "alkalinity" and "buffering capacity" are used interchangeably. Although technically not the same things, they are equivalent in practice in the context of fishkeeping. Note: the term "alkalinity" should not be confused with the term "alkaline". Alkalinity refers to buffering, while alkaline refers to a solution that is a base (i.e., pH > 7).
So, With all that in mind now lets talk about the benefit to using Distilled water in water changes.
If you use Distilled water or even R/O water during you water changes you will be able to slowly and safely reduce your pH while maintinaing your tanks buffering ability. So, instead of paying 200.00 for an R/O unit go to the store and pay 59cents for a jug and use it to top of or do water changes. As water evaporates from the tank the water left in the tank becomes harder due to the minerals being left behind. This alone is a good reason to use Distilled water.
Now I am not saying to use a pure R/O tank or pure Distilled tank as both are not good for your tank. What I do suggest is to use it for top offs and partial water changes. Aslo, with partial water changes add a little tap water to the mixture to keep your buffering high.