There are really two issues, flow (volume) and pressure. They are of course related but not the same. The answer to your question is that the injectors control the flow as dictated by the computer. However, they don't really meter volume. The computer relies on the fuel pressure to be at a certain level so that when it opens the injectors for a certain period of time, they deliver the required volume. So, there is also a fuel pressure regulator that holds the pressure constant regardless of demand, therefore it too plays a role in flow control.
When you go to a fuel pump of greater capacity and/or pressure, the regulator still does its job, but the "bigger" pump allows you to increase demand without flowing so much that the pump can't keep up, thereby causing the pressure to drop and supply fall behind demand.
Make sense?
One thing to watch out for with higher pressure pumps is that the stock regulator has an orifice that allows excess fuel to bleed back to the tank. A pump of greater capacity and pressure can overwhelm the orifice and cause pressure fluctuation, so a new regulator is recommended. AEM has a nice direct replacement.