Sorry, I was working off the premise that her heart/lungs may have been harvested during organ donation surgery. You are absolutely correct on the other provided the heart and lungs remain.
From the organ transplant surgeries I have witnessed, where heart, lung, kidneys, liver etc were donated, time of death was called as soon as the vent was shut off as there was nothing remaining to keep the patient alive.
I was questioning how the coroner could determine time of death if she was alive at the scene. In order to donate organs, you still have to have a blood pressure and be breathing, otherwise you have about 4 minutes before organs start to die and be unusable for transplant. There are very strict criteria for organ donation as you can imagine.