It doesn't matter if NC State vets "never intended to hurt that dog". It was pure negligence on their part. If it had happened at a human hospital, and they had placed a feeding tube in a human's trachea instead of their esophagus, would it have carried more weight with you?
Negligence is negligence. Lacie's life was cut short, and her owners have experienced, and will continue to experience, pain and anguish because of her passing. NC State should pay, and they should make certain it never happens again at their facility.
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