The details of shipment and arrival are usually contained in the IDPF for the individual concerned.
In the IDPFs I have consulted on various repatriations it seems that these details are well documented, containing copies of correspondence between funeral director and the Army, etc...
In the cases where the casualty was to be buried at a Stateside military cemetery, I find that in all cases the individual was received by a local funeral home.And regardless of whether the casualty was to buried at a military cemetery or civiian cemetery, there was a military escort--usually one service person-- assigned to the body from arrival at a Stateside receiving facility right through to burial.
In several cases I find where the funeral director or family forwarded a letter of thanks to the Army for the services of the escort, and the return reply from his CO usually references that the thanks of the family will be relayed to the escort, and a copy of the families letter placed in his service file.
I had the opportunity recently to speak with a local funeral director who had been with Mortuary Services during the Korean War, and he told me that on receipt of a casket at a funeral home Stateside, it was NOT standard procedure to open a received casket for additional identification of the remains.