"Pure" is ambiguous. If they mean that it only contains water (as in H20) then no, it cannot be purer than synthetically purified, deionized water. But purfectly pure deionized water is non-potable. Not sure how you define purity in drinking water but it's certainly not the same as you define it in the lab.

"even its gas is natural"

What in the world does that mean? Is there water out there that has synthetic gas?