Suffice to note that there are entire undergraduate engineering courses on fluid dynamics.
In this context, fuel pressure is dependent on flow and restriction.
Of course it is the pump that provides the flow. And I have no reason to doubt that the fuel pump will pressurize a completely closed system to about 4.5 Bar, after which it cannot further provide fuel.
The maximum flow rate that a pump is capable of producing requires no restriction. So if the fuel pressure regulator were removed from the system, the pump would be pumping a high amount of fuel through the system, back into the tank, at a low pressure. The low pressure would then not be sufficient to provide the metered amount of fuel through the fuel injectors.
Fuel pressure regulator stuck closed = very high pressure (thanks to the pump) and consequently overfueling through the injectors.
Fuel pressure regulator stuck open = very low pressure (despite the fact that the pump can pressurize up to 4.5 Bar) and there will be underfueling.
So both things can be correct: the pump provides the flow, but without restriction via the FPR, the pressure will be LOW.
And really, this is an academic point: I’m sure all will agree that without a specific fuel pressure (fuel provided by pump, pressure regulated by FPR) the injectors will be unable to provide a precisely metered amount of fuel, required for proper combustion in the cylinders.
I appreciate internet arguments. They occupy me on some Sunday mornings.