My guess is that she doesn't trust the tap water anymore. She's seen your reaction to the brown water. She's probably overheard comments that enforce her perception that the water isn't good. It's sometimes difficult to logic-away even adults emotional reactions, especially ones that have been reinforced. Don't turn it into any more of a power struggle than it's already inadvertinently become. Make a big deal about buying her "special" water because you've notice that she doesn't seem to enjoy your tap water. Buy one or two gallon jugs of your favorite brand of bottled water and put her name on the outside with magic marker. "Kristen's special Water". Make sure she sees that the water came from the store instead of the tap. Hold the water up to the light and comment on how wonderfully clean and clear and tasty it looks.
When you give her water, make a big deal about pouring it from her special bottle. Don't let the bottle get empty, but don't let her see you filling it from the tap, either.
You may also consider making sure her children's multivitamin includes zinc. For whatever reason, if you aren't getting enough zinc from your diet water has an off taste. A support group member gave me that advice and it worked for me!