Consider that the dispatcher pushing for acceptance of the flight plan boarded the flight! That must have been somewhat persuasive that he knew what he was doing when he filed the flight plan.
Sure, the numbers were wrong, but those are just numbers. Who really flight plans 4:22 with 4:22 fuel on board? What, they were planning on being towed off the runway? So the woman accepted the flight plan with this tell-tale mistake on it, when she should have made that fool dispatcher come back with one reading 3:52 and 4:22 instead, as I suppose he would have done.
The Swiss cheese model does not work when there's criminal negligence involved. If there's one guy not playing by the rules, then the system breaks down very easily.