Having your tonsils removed is a routine procedure. You aren’t supposed to die.
Morbidity/Mortality
Morbidity other than minor post-surgical infection is uncommon. About one in every 15,000 tonsillectomies ends in death, either from the anesthesia or bleeding five to seven days after the operation.
http://www.surgery.com/procedure/tonsillectomy/morbidity-mortality
Death occurs in 1 in 15,000 tonsillectomies. Doesn’t that tell you that even the most simple of surgeries can result in death? No surgery is routine regardless of the simplicity. Complications, including death, can and does result in any surgical procedure to patients every day.
The surgery wasn’t a routine tonsillectomy. The child was obese; the surgery was in part designed to address her severe sleep apnea. So it was complicated. Complicated surgeries often result in less than desired outcomes. Whether or not the hospital or any medical professional was negligent remains to be determined.