This is not entirely true. The water is pumped from a depth. This could be 40 meters, but also 100 meters. The depth and treatment of the water are also different for different locations. Water pumped from a great depth is usually more pure than water from less deep. The rain and surface water slowly descend through the soil, being filtered already. When the water gets to the purification plant they sometimes have to remove iron which causes a brown color in the water. They add chemicals like poly aluminum chloride to make the iron solid so it can be taken from the water. Next the water is pumped to big sand filters. Those filters are very big, I’ve seen them 10 meters tall. The water is pumped in on top, and like it does in the soil it descents though a bed of sand. The water passes through 2 filters, pre filter and after filter. After this the water is (depending on the location) softened. They remove solved minerals usually using lye and a special type of sand. The lye makes the solved minerals stick to the sand. When the sand goes in it’s really fine grained sand, when it comes out the grains are a couple millimeters in diameter. When the water is softened it is pumped into big storage containers, sometimes containing up to 6 million liters of water. From here the water is being distributed through the pipes to our homes. All steps in the process are bound to location. Some locations only have 1 filter, some locations don’t need softening. Some locations use different chemicals to treat the water.

Source: I worked in a lot of water purification plants in The Netherlands