I've heard concerns that straight distilled or DI water might not be a great idea. I've heard of this black gunk forming due to the acidity on aluminum parts. It's acidic (carbonic acid) due to dissolved CO2. I figured if I ever wanted to flush with distilled water, I'd add a little bit of coolant to neutralize the acidity.
I live in an area with Sierra snowmelt as our primary water supply, and the hardness is ridiculously low. I've used distilled water to mix coolant, but had no qualms about flushing the system with our tap water. The last time I had someone replace a radiator, I didn't worry about if he used tap water, since we have good quality water.
I've also lived in a city where most residences get well water from city wells. Foulest stuff I've ever smelled probably due to sulfur content. Anyone who washed a car made sure to dry off quickly before it crusted. There was literally calcium/magnesium caked everywhere including faucets and a hard ring around toilet bowls. I would never even think of letting that stuff near my cooling system.
However, you might want to simply add what you think is needed to balance the remaining water, then fill with 50/50 mix. That's if you use an uncut coolant rather than a premix. There's lots of coolant out there that only comes in premix these days.