I'm quite happily using water from our well(pH 7.6, hardness 74ppm, sodium 18.4mg/L, no appreciable sulfate, iron, or manganese) and brewing mostly japanese greens.
I certainly believe that the water used has an effect on the results when brewing tea, however like several commenters over there I find their "test" to be of very little value as "tap", "bottled", and "filtered" each represent thousands of different waters and they've used 4. Then there is the question of how a specific tea interacts with a specific water using a specific brewing method. For instance their tap water scored poorly with their black and had top marks with their oolong, either they've shown it's impossible to say "use <whatever> type of water when making tea" or they've shown their test has noise in it and isn't saying a damn thing.
Beyond the limited value of their test, bottled water is an ecological disaster and not a great economic choice if you're going to consume a significant quantity of it daily so there's no way no how I'd be using bottles of water for my daily tea. If I'm ever faced with tap water that's vile I'm sure something could be made to work with filters even if they claim their specific combo of their tap water and their one filter didn't work out for them.
I also just noticed that right below this thread is an older one about water http://www.teachat.com/viewtopic.php?f=41&t=19701
that one also has links to a couple of other threads on the topic