Another reason this wouldn't work is that the organs were without oxygen for too long. The body must be put on life support almost immediately to keep the organs viable until they are harvested.
The woman's plan of putting an Organ Donor sticker on a victim's driver's license wouldn't have actually worked, since the person has to be in the state's computer system when the person registers to be a part of the organ donor program. Since they would not be already in the system, putting a bogus sticker on someone's D.L. wouldn't have work.