There are a lot of websites that quote the same incorrect information regarding distilled water in soda and mineral leaching. If this were true, and it is not, would be leached and water with sugar, or artificial sweetener would become heavy. If you are concerned, add 10mg Na to each liter. Also, eating food with water, all minerals are mixed with fluid in the stomach converting distilled water into mineral water. Distilled water is not magic, if you add a splash of milk to tea made with distilled water, you now have 10x the calcium of regular mineral water.
Distilled water is very good for you. The only areas it may cause a problem is developing nations that have near famine conditions. For the rest of the world who usually ingest 15x the sodium recommended, distilled water leaches salt first. ONLY IF you are salt deprived (extremely rare) will distilled water leach excess potassium and or calcium.
You would need to drink about 2 gallons in 10 hours for there to be a problem.
If heavy sweating, water of any kind is only a thirst quencher or temporary fluid fix. Most people can afford 7 pounds of sweat (near gallon) replaced with only water before electrolytes become an issue. At that point, electrolytes are needed regardless of water type ingested. Mineral water has very small trace minerals and represents a small fraction of where K, Na, Ca is absorbed in the body. For you to get your average daily requirements of Ca and K from water alone, the water would taste terrible.