The main point with all of this is that someone is only dead when a Doctor says so. No matter what the obvious signs are intil a doctor certifies life exstinct you are alive legally.
The best example of this is when someone died alone and is not found for some days, weeks, months. The date of death will be the date they are found.
For any airline it is far better to continue to destination where they can be assured that the correct services are available rather than divert and leave someones loved one in the hands of the unknown with the difficulties of then getting the deceaed repatriated to their loved ones at home.