Trouble is, Chris, you really don't know if that purified water still has a high pH or phosphorus in it. Our (very good tasting) tap water here has naturally occurring phosphorus in it and the pH is around 7.8 which is a little high but not impossible. My well water is pH 8.2 and has a lot more phosphorus so it really isn't all that great for watering plants. Does your fridge have a filter and water dispenser on the door? That water is probably purified just as much as the water you're thinking of buying, and will cost even less. But you still don't know what's in it or the pH.
Both those things, if too high, can make it difficult or impossible for plants to take up certain nutrients. The phosphorus is known to "bind" or chemically combine with some metallic ions like magnesium which makes them unavailable to the plants.
So, at least until your plants have recovered from their present precarious state, I'd stick with distilled water, when you fertilize or spray with Epsom Salts solution.
Lucky for me, I have lots of rainwater to use for dissolving all my fertilizers and additives into and the pH of my rain water is 7.2 generally. Rain water is essentially distilled by nature, but then it falls through the polluted air collecting "stuff" so not entirely pure but usually the next best thing - and free! Is there a down spout on your house that you could put an old garbage can under, to collect the rain and dew off your roof? You'd be surprised how little rain will fill up a 35gal. container.
