There was no need to argue over jurisdiction. It should have been a joint investigation from the start.
The CBI needed the cooperation of the Military Police for the investigation on base, and the Military Police needed the CBI's authority off base as they have no jurisdiction over civilians.
When Sgt. Hawkins is in the Armory he pulls back the bolt of the M4, to check if the chamber is clear before placing it on the rack with the magazine still in it. No soldier would do this. The weapon would be made safe by removing the magazine and clearing the chamber before storing it.