Bob Nuckolls commented on the fuel pump fuse blowing HERE
This is my interpretation of what he posted:
The solenoid coil that drives the pump piston can draw up to 12 amps. But since it is only turned on for a very few milliseconds out of each pump cycle, the 5 amp fuse does not get hot enough to blow.
The fuel pump internal solid state controller temporarily fails at some low voltage point while cranking the engine with a nearly dead battery. Instead of turning on the solenoid coil for a small fraction of each pump cycle, the malfunctioning controller turns on the solenoid coil and leaves it full on. The duty cycle is then 100 percent at 12 amps which blows the fuse.