Well, I was recently unlucky enough to gain some first hand experience with this subject (See Scuba Accident Thread)
All things considered, I don't think things could have gone any better or faster in the US.
My buddy died in a scuba diving accident at approximately noon on Monday, that same night the autopsy was performed and he was embalmed. Tuesday was spent doing paper work and talking to the US Consulate. Wednesday morning he was on his way to the border in Lukeville to meet a hearse from a funeral home in Tucson.
72 hrs. from time of death to being on US soil; including an ambulance ride from Las Conchas beach to Santa Cecelia Mortuary, Autopsy, Embalming and a trip to the border for $1,200 usd.
That could have easily been a $20,000 bill in the states.