MOSFET as a switch. Why does the voltage depend on the gate?
The illustration is correct. VGS must be above Vth for the NMOS to be ON, otherwise it will be OFF. Therefore in your circuit the maximum possible voltage at the source is VDD-Vth, otherwise the NMOS would be OFF. Note that in your circuit VGS=VDD-(VDD-Vth)=Vth, so it is ON, but the voltage at the source cannot increase further because it would turn OFF the NMOS (and the source voltage would decrease, turning it ON again). It therefore comes to an equilibrium where VGS=Vth. 

The fact that there is three NMOS instead of one doesn't change this situation, because all 3 NMOS have the same VGS voltage.

If you want to use an NMOS as a switch and have the full VDD on the load you should place it in the low side as in the following picture.







simulate this circuit &ndash; Schematic created using CircuitLab