Maybe this is an over kill comment, but in this day and time, even manufactures (aka store bought filtered water, J&J,etc) "might" have contaminates in it from the processing plant as it comes in those plastic jugs/containers! In reality....Who knows what in the container as we have been a trained society of zombie sheep to trust manufactures and whatever we buy or purchase right out of the wrapper.
Filters water itself may be fine, but Distilled water has less contaminates and minerals in it than filtered as that is a different process. Thus for me, Distilled is a better bet.
Distilled water removes a lot more minerals (contaminates) than filtering, that's why labs only use distilled and de-ionized water, its more contaminate free/pure. I see distilled water all the time for around $0.80 cnts a gallon, cheapest auto tint insurance you can buy. But you still have to gamble on the container it comes in being contaminate free as well.