If he died in the airport before boarding, they were probably smart not to say anything until they got to LA - it ended up being the quickest, least expensive, and most dignified way to get him home. Think about it. Had anyone noticed that he'd passed or said anything, he would have been removed from the airport, taken to a morgue, investigated (possibly autopsied) - the kin would have had to contract a funeral home in AZ to arrange for shipment home (probably in a body bag in the cargo hole), the tickets they had already paid for may have not been refundable (they don't automatically refund those anymore even with a good excuse), which would also mean the purchase of new tickets to get themselves home (I don't know the family but when you're battleing some of these illnesses, it drains your bank accounts).
As it happened, the family could pretend he was still with them a little while, they got to supervise his trip home, and no one else on board were the wiser until they arrived. I just wish they had kept quiet about being suspicious that he'd passed on before boarding - they may now be facing some sort of criminal charges and some prosecutors have nothing better to do with their time nowadays than get get publicity with these types of unusual cases.