Pumping the gas does not add fuel into the lines. The gas is already there, or should be, under pressure. You could pump that pedal forever and all it does is work a little flap, which in turn sends a signal to your car's computer. Your friend is thinking back to the dark age of carburetors, not fuel injection.
Sounds to me like you have a hard-starting problem, either due to needing a tune up, or perhaps a faulty fuel pressure regulator. In either case, there is either not good enough spark (tune up problem) or not enough fuel (fuel pressure regulator problem) to ignite the fuel and start the engine promptly.
The rough running you experienced when it finally did start was probably due to persistent cranking of the engine, and the car's computer (not your foot) injecting more gas into the cylinders as you crank (it would do this whether you pumped the gas or not) . This "floods" the cylinder with gas and makes it harder to start--especially true if the tune up parts are not up to snuff. OR....your car started roughly because of fuel starvation---the fuel pressure regulator doesn't keep enough pressure in your fuel lines overnight, or after sitting a couple of hours, so your poor fuel pump has to pump gas all the way from the back of the car to the injectors. With a good fuel pressure regulator, you'd have enough pressure already in the fuel rail, ready for the injectors to open.