While the death of a pet is always a terrible thing, flying has inherent risks and flying with a pet has rules. The rules for flying with a pet are agreed upon when you pay the fee to bring you pet aboard the flight. She knew her dog would have to be A: in a carrier and B: placed under the seat in the row in front of her.
It wasnt the airline that killed her dog, it was a combination of unfortunate circumstances that did it. As always...this will be a PR mess.