Question:
We are looking for another source of water. The only water I know that's likely to be pH 7 is distilled water. The question I have is this: if we treat pure, sterile, non-ozonated water with a little aquarium salt, a little AquaPlus and Cycle to introduce bacteria, will it be safe for a betta? The pet shop told my girlfriend that distilled water is too sterile and pure, end of story

Answer: Distilled water is dangerous. I don't know how much better it would be even with the aquarium salt, but the osmotic pressure/hardness of the water might still be too low to be safe for the fish.

I was actually having the opposite problem with my pH being too high as well as too hard. Using filtered water actually fixed the problem, and I keep a really close eye on water hardness. I would suggest you get a water testing kit. Setting aside any current debates on their true accuracy that have been running lately in the website, it's good to have. If you still doubt your water purity after that, my LFS guy who really hasn't steered me wrong in the past recommended Deer Park. Expensive, yes, but if you're that concerned it's water quality, probably worth it.

I would recommend a good fish book (love my 'Aquariology'and 'The New Aquarium Handbook' books) to get in some research on water quality and what to look for.