One of the things that tickles me about mineral water is that (at least here in Germany,) bottled water doesn't have to meet the same standards as tap water. Most folks still prefer mineral water here, though.Food has to be standard. If a label says "0.1g calcium", the bottle has to contain 0.1g of calcium, within certain error limits. Water coming straight out of a spring has no such regulation and so different bottles could contain thousands of times more or less than is claimed, which is illegal in most places and could be very dangerous. This isn't a problem for some mineral water, where the minerals are simply added in production. For water that is advertised as containg naturally occuring minerals however, the water must genuinely contain them naturally, so taking them out and then putting them back in standard amounts is the only solution, or at least the only one that I know of. I can't guarantee this is true for all mineral water, but it certainly true for a lot of it, and it seems a reasonable explanation for the wording on the Armenian label.
It is indeed very silly, but with the hang-up people have with the word "natural" these days it is presumably still profitable.
One of my favorite incidents with the mineral water/tap water thing occurred here in a small village. The local water supply was from a well that was drilled in the village. The water was piped to all the houses, so it falls under the tap water laws. The water wasn't clean enough to meet those regulations, so the federal government told the folks they couldn't use their tap water for drinking or cooking. The tap water did meet the less strict bottled water requirements, though, so the folks just got themselves some bottles, labeled them "Natural mineral water" and filled them from the tap. When anybody came to check, they'd find the village folks all drinking and cooking with bottled water - all copacetic.
This story was on a TV program about ten years ago, and the program was about highlighting stupid bureaucratic non-sense. I expect the situation has been changed, but it was funny.