Burn victims are often conscious and moving initially due to the effects of adrenaline, pain etc and in her case perhaps the drugs in her system. They then soon expire due to various things like sepsis, neurogenic shock, hypoxia etc etc Have seen and transported several burn patients who were alert and somtimes combative like her, who quickly lost consciousness and passed quickly at the trauma center.
In her case the thermal lung injuries most likely caused the gradual lessening of O2 transfer to her blood and buildup of Co2 which probably in short order rendered her unconscious and shut her brain down. Only reason she "lived" so long was due to artificial life support measures to gauge the viability of tissues etc for donation.
Only reasons I can see for them covering her entirely like that was either they were aware who she was and that paparazzi might be there or they were trying to totally cover her to avoid on scene contamination to her burns.
