Not to mention Chip, what water hasn't touched some sort of metal surface? Surely tap water has!
The only argument one could make is that the metal infuser when in contact with tea water can effect the taste. I, however, do not believe it does.
How do you know if the rainwater is safe to drink in your area? Because if it's clean where I live, I could (1) collect it in a sheep's stomach, (2) pour it into a ceramic vase (3) place said vase into a pit-fire in my back yard (4) pour 170 degree rainwater into my Tokoname teapot with clay sasame (using hemp oven-mitts), and (5) decant my meticulously prepared liquor into a steel mug....no wait, a porcelain teacup.