Wrong:

In this picture, we have combined a boiler with a standard faucet:

As it only has 2 connections, the water (1) is distributed to the faucet as well as to the boiler using a T-manifold. As you can see, the full line pressure hits the water tank (gray); it will be lowered only while the hot water outlet is opened (2). You could decide to add an extra, external valve to the system to lower the line pressure to a minimum, but it would still be persistant - sooner or later this tank will burst!

Correct:

In this picture you can see what the third connection of a low-pressure valve is good for:

The water first flows from the line connection (1) into the faucet, where it is blocked by the valve (curved blue arrow). When you open the hot(!) water valve, fresh water is flowing through hose (2) into the tank of the boiler - and displaces hot water via hose (3): The tank will simultaneously be re-filled while taking water out if it!
It is important to understand that only a small fraction of the water line's pressure (1) hits port (2) and is forwarded to the water tank - therefore the term "low-pressure"! If the hot water valve is closed, the tank's water supply is completely interrupted, and the tank is depressurized.

The fine tuning of the water temperature is done in the way that some fresh water (from 1, dotted blue arrow) is mixed with hot water from the tank. This technique is possible because (as already explained above) the water line provides a lot more pressure than necessary to refill the tank.

If only cold water is needed, the water runs directly from (1) through the valve, without going through the reservoir.