Let me assure you, as an old desert rat that when you are really, really thirsty, "flat tasting water" will be the least of your concerns. Even under normal circumstances, I have never understood the problem, but my wife asserts that my taste buds were shot off in the war....

Purifying water from a typical babbling brook, I set up my canister stove, boil a pot, decant it into a canteen which is immersed back in the babbling brook, while pot #2 comes to a boil. My boil times approach those achievable with a micro wave (within a minute or so). Besides, the cup of hot water is readily transformed into a nice cup of tea, the elixir of the gods.