These might be the health risks talked about...
*Many reverse osmosis systems remove the good with the bad. Iron, calcium, manganese, and fluoride are a few of the beneficial chemicals that may be removed, depending on your system. Removing these essential elements from our drinking water doesn't pose much of a problem, since a well-rounded diet will provide these as well. However, many Americans do not eat a diet that is rich in vitamins and minerals. If these people also drink demineralized water, then they are more prone to vitamin and mineral deficiency.
Additionally, when used for cooking, demineralized water was found to cause substantial losses of all essential elements from foods such as vegetables, meat and cereals. Such losses may reach up to 60 percent for magnesium and calcium, 66 percent for copper, 70 percent for manganese, and 86 percent for cobalt. In contrast, when hard water (not treated with reverse osmosis) is used for cooking, there is minimal loss of these essential elements.*
...I agree it probably isn't relevant if you only drink it when you travel though.