Water can make a difference, but not in the way Knowledge is King describing. De-ionized or overly filtered water (the empty school bus in the analogy) won't actually extract much at all. I don't claim to fully understand the chemistry, but anyone who has ever attempted to take a shower with really soft water should be able to attest to the fact that it's terrible at dissolving solids. If you take a shower with really soft water, you get that feeling like you can't quite get all of the soap to wash off. Trying to make coffee with really soft water is similarly problematic - extraction will be very slow and uneven.
Of course, a similar explanation might hold true for coffee. But just because the soap effect is true doesn't mean much regarding coffee.