That's because there is no specific disease. Just like they aren't allowed to feed beef to cows for fear of spreading Mad Cow (a prion disease), they aren't allowed to process sick or "downer" cows. Obviously, this is because they may not know why the animal is behaving that way or if it is contagious. It could be a spontaneous re-emergence of Mad Cow or some other malformed protein for all they know, so it's a "better safe than sorry" rule. Obviously, some of that meat ended up in the supply that shouldn't have.
IIRC, it was determined the guilty prions found their way into alive cows by feeding them parts of dead cows, especially the brain.
Anyone know if that is still allowed for cows that are not bred for human consumption? I wonder if some meat that came from non-human-consumable cattle ended up in a batch of death pockets to save $0.005 a pocket.
Along the same lines, the Kuru epidemic in Papau New Guinea was traced to prions and tribes tradition of cannibalism. Like Mad Cow, humans would shake uncontrollably and exhibit other like symptoms. There is a very very good documentary on the Australian doctor who dedicated his life living with these tribes to battle the disease. Even 50 years later having it under control, he still expects it to resurface due to the incredible incubation period and the nature of prion related disease.
In humans, the incubation period is much longer than mad cow, it can be 50 years or more!