@versub
Can't say I know about it taking away minerals. Likely pure (distilled?) water does less for the body, and just passes through the system easier, than when there is something for it to latch onto. I don't think using a purer water would make the tea less healthy.
@Amenohi
Perhaps she does enjoy the flavor. Frankly, I see it as her enjoying the exclusivity of it more than how it tastes (thus ruining the tea). People enjoy expensive wines and booze, when it has been proven that cheap popular brands taste better. I've got a lot of calcium in my town's water, it kind of shocked me when I could taste a considerable difference when using the long-life brita filter (removes more than their normal one). If I'm just enjoying the water though instead of tea, I typically add something like peppermint or orange extract. Pretty good by itself though. Even use it for cooking when I can.
I just can't get the image of her drinking hot spring water with sulfur and other minerals out of my head. I know it is likely an exaggeration, but I care about getting the most out of the tea leaves, and not the flavor of the water.