I'm certainly no authority on the matter of handling deaths at sea, and any observation upon the actions of the captain of the boat is pure speculation, but I imagine the captain of the boat was considering the jurisdictional aspects of the death and so forth.
Immediate notification of the authorities would serve no practical purpose. There may be some legal issues involved with not reporting the death immediately, but I don't know.
If I were the captain of a boat out of an east coast port and was in international waters between Florida and the Bahamas, then I would probably do the same thing.
The U.S. Coast Guard has no jurisdiction outside of territorial waters so they would not be involved in launching a boat or helicopter to recover the corpse.
Sometimes things are just best handled quietly and calmly.
My condolences to the divers family and friends . . .