>water without minerals upsets the osmotic balance and leads to lysing (rupture) of the cells lining the stomach
I've heard many people claim this but I've never seen any convincing evidence that it actually happens in vivo. Even if you pour it directly down the throat, ultra-pure water stops being ultra-pure as soon as it hits the stomach. There's no way it can touch any gastrointestinal cells before it's contaminated.
Your linked article even acknowledges this. "currently available data have not unambiguously demonstrated a
direct negative effect of low mineral content water on the gastrointestinal mucous membrane." It also cites an animal study showing no damage:
https://www.ncbi.nlm.nih.gov/pubmed/8434446
Water can be an important source of dietary minerals, but the health impact of this depends on what else you're eating. I agree it makes sense to have minerals in drinking water, for the taste as well as the possible health benefits, but missing them is not actively dangerous.