Copper in the water is not a problem. In fact, in moderation it is necessary for your health. In the United States, a lot of homes use copper plumbing. However, the concentration of copper can be an issue, and letting water sit in copper containers is, in fact, a risk. The average concentration of copper in tap water in the US is between 20 to 75 parts per billion. It can even range up to over 1000 parts per billion.
To avoid copper toxicity, the concentration of copper in drinking water should be kept below 1300 parts per billion. Tap water can get a high concentration of copper from the water sitting in the pipes overnight. This is what leads me to believe that storing water in copper vessels could be a bad idea. Children under one year old and people with Wilson's disease are even more sensitive to the effects of copper, and keeping the copper concentration below 1300 parts per billion is not enough.
Water stored in a copper container reaches 180 parts per billion in about 16 hours. This amount will vary depending on conditions and the amount of copper already present in the water.
Corrosive water and hot water can also lead to higher concentrations of the copper being absorbed.
Over time copper does form a natural coating that prevents as much leaching into the water, but this does not prevent it completely.
OPINION: Based on this information, I would advise against storing water in copper containers at all. If an older container that has had time to develop a coating is used, and the water is not left to sit in it overnight, there may be less risk for the average person--but I would definitely not use this with children under one year of age or those who have Wilson's disease.
The ideal solution would be to test your water for the level of copper and ensure that it is safe.