Your tester doesn't require a good solid ground to read 12v, your pump does. If you've got a broken wire, a corroded connection at the frame or a loose connection at the pump it could be making enough connection for a reading but not enough to flow the amount of juice the pump requires.
Do you have a fuel pressure tester? If not Harbor freight has a cheap one that works.
Run a new ground wire from the ground on the pump to a clean spot on the frame. If it starts working then you had a bad ground, if not then run a wire directly from the battery to the power lead on the pump. If the pump doesn't run or puts out too little pressure then your pump is bad.
"But it does me no injury for my neighbour to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg." - Thomas Jefferson, Notes on the State of Virginia, 1782
Arguing with a truck driver is like wrestling with a pig in mud, eventually you realize the pig enjoys it.