If there's a strongly enforced ban on civets,I would bet many of the hunters or trappers in Asia would just skin the critters and sell them as something else or smoke,salt,maybe jerk the meat to change its appearance.
Even if the meat was fully cooked by the trapper,the person that skins the animal would be most likely to get the disease.
I don't know how they trap over there but I would guess snares are used much of the time (cheap and easy to carry a lot).To just release an animal caught in a snare would put a person in contact with saliva and probably blood being slung around.
Some people can't follow game laws here.In Asia?No way!
The Chinese people are plenty afraid of SARS. If they were told that the civets cause it, I think it might have some impact.