Is it possible for a toddler to kill a cat?

When my daughter was about 2 we adopted a male, almost fully grown cat from the rescue centre. He had an unusual personality, extremely placid and laid back. He was really lovable but seemed less lively than most cats. Then something happened which saddened our family very much and made me reluctant to own a pet again. One day my daughter picked the cat up by the neck. The poor animal lost control of his bladder. I thought it was strange that he didn't struggle to get out of her grip. He just dangled and didn't even try to get away. After that the cat continued to urinate on himself and we cleaned him and put him to bed intending to take him to the vet in the morning if we needed to. We thought he would be fine but he didn't make it through the night. My daughter has always felt guilty about killing the cat and her sisters tease her about it. I felt guilty for not supervising the kids with the cat but I never thought something like this could happen. I try to make my child feel better by telling her it would be impossible for a kid so young to have the strength to kill a cat. (maybe yes, if it was a helpless kitten). I think this is probably true as a normal healthy cat whose life was in danger would fight with teeth and claws. We think the cat may have been sick to begin with. Would any cat experts agree? Otherwise she will have to live with the label 'cat killer'.