I'd say it's about fifty-fifty, the guys that have swapped out the pump and fixed the problem and those who have swapped out the pump and then had to find the original problem.
When you turn the key to run, the fuel pump relay will close for a second or two (if you hold your finger on the relay you can feel it click), just as a prime, it doesn't really build much pressure. It builds enough pressure to get just a slight squirt if you depress the shradder valve. During start, the fuel pump relay closes and supplies power to the ballast resistor relay (the ECU closes the relay), which bypasses the ballast resistor for the start, then you get pressure. If the ballast resisitor is bad, it will start (likely) but won't run and will shut down as soon as you release the key. The ballast resisitor is bypassed (through the ballast resistor relay) when the key is in the start positon.
The dark green and black wire at the resistor, is the pump end of the resistor and should have power, for a second or two, when the key is turned to run and during start and with the key in the run posiston after the motor is running.
If the fuel pump relay isn't actuating, it's usually because the ECU refuses to actuate the relay, bad CPS, bad Cam posiiton sensor, maybe the MAP is getting no mean atmopheric pressure index signal and other stuff.
There is also the off chance that a connector is corroded (no power to the pump), a relay is flacky or the pickup tube on the pump is falling apart and there is a hole in it.
Or maybe a bad pump. Changing out a pump is a beatch. I'd sure as heck make sure I'm getting juice, before I went through the convulsions of changing one.
I've had fuel problems on three different XJ's (sometimes multiple problems with different causes, at different times) and haven't replaced a pump yet. It always turned out to be something else.