OK, I think I need to clarify my intentions a little more... I know that my tap water, or spring water, or filtered water, are all fine for brewing. I have made a few batches with each, and they all turned out to be good beers.
Malt extract is made by reducing/evaporating much of the water (or all of the water in the case of DME) from a large batch of wort. All the salts and minerals from the complete wort remain in the reduced malt extract--they are concentrated, just as the malt sugars, and flavor and color compounds are concentrated in the extract. In order to get back to the exact characteristics of the original wort, you need to put back in exactly what was taken out--pure water.
If you add any additional salts or minerals via the water you add to make your wort, you are changing the flavor characteristics. I'm not saying that is necessarily a bad thing, but it is another variable that you would need to consider in the planning stages. Going with distilled or RO water makes it much easier to predict what the final product will taste like.
