How do you people think water towers work? They use pumps to get the water to that height in the first place, which, in a power outage, can fail.
The only reason you don't see a difference in a power outage is because the towers are designed to hold enough water to supply the community for a day or longer, and power outages are usually resolved in that amount of time. And if there was something seriously wrong and it would take much longer, they could always use generators to keep the system going since water supply is a top priority.
In places without water towers, or pumping stations that provide it for you, you'd need another way to get the water into the building. A private pump that brings the water from a well into the building and stores it somewhere where the normal pressure system can do its thing. Just like how a high-rise building will have at least one little water tower on its roof, since the city system can't generate the pressure needed to get water up to the top of each and every building.
The only problem with this kid's understanding of the system is that he seemed to think each fixture had its own pump under the floor, instead of having one pump bring it into the house and store it somewhere, where it could then be delivered to each fixture with pressure.
If he does have a system that uses well water and a private pump, instead of a public pumping/water tower system... The reason the toilet still worked was probably because there was still water in the house tank. If he kept flushing the toilet or using other fixtures in the house, the water in the tank would eventually lose its pressure as it runs out and they would all stop working. When the power goes out, it just stops the pump from bringing water to the tank, it doesn't stop the pressure/gravity process from delivering that water to the fixtures.
