Guess you missed the part where I said I had to "hold and store" them, didn't ya? And there were only 3 people on the entire ship that were allowed to be in the office when I was processing them, the OIC of the MILDET, and the Chief, but that was only while I was awaiting approval from BUPERS to handle them by myself (still had to have an E-7 or higher until I was granted access). But, after BUPERS sent me the authorization, I was allowed to handle them all by myself. That meant storing, handling and processing them. And yeah, if I had a dream of spending my time in Leavenworth, it could have been very easily realized by not handling them properly. But, I liked my career and liked filling an E-7 billet as an E-6 (positional authority is a neat thing to have). Did so well on that tour, that I was offered another Chief billet (also independent duty) as my follow up tour at a MEPS, then I retired.
As far as having the authority to keep those documents after he'd done what was needed? None. Yes, I will say that he was sloppy and mishandled those documents. If I had kept any part of the exams (especially the classified ones) after I finished processing them, I would have lost my career and been sent to Levenworth to finish out my enlistment and kicked out with no retirement. Yes, I understand VERY well the procedures required for handling classified information. But, here I am, happily retired and satisfied knowing I had an excellent career.