This is correct. Water can only flow two ways: it can be pumped upwards, or flow by gravity downwards.

What you described is pretty typical. A community will pump water up to an elevated tank, then let the water flow by gravity back down into town. This keeps the pumps running less and provides a good, usable pressure.

In some cases there is no water tank to feed an area by gravity, and instead water is pumped via "booster pumps" into the area, with the pumps providing operating pressure. These are generally very small parts of a town at an elevation higher than the storage tanks. So unless you live on the highest hill/mountain around town and can look down on everyone else and the city lights, you probably aren't in such an area.

Where you might run into a problem (in either case) is if the electricity to the pump stations go out and/or there is no backup generator, or the generator has run out of fuel. In that case the water department might (hopefully) have a backup connection to another water provider or system for use during emergencies.