I'm not sure it was all that fast. If you're not going to embalm a body, cremation must occur pretty quickly or it gets pretty nasty.
The autopsy got all the information they'll ever need to answer questions.
My husband was murdered, and they held his unembalmed body for over 2 weeks. One of the reasons for holding his body was for retesting.
BTW, the cause of death in Louisiana is public, and his was published in the local paper.