The people u spoke to have the same clearance as former presidents? Or u friends with Barry and asked him the SOP for retired presidents?
Depending on the classification level and programs involved, some documents are marked with a classification when produced, but can be downgraded AUTOMATICALLY with no complicated process involved.
The producer of the information decides if it's classified based on guides and documents that say so. Most documents I worked with say "Declassify by OADR", meaning the Originating Agency's Determination is Required." If the docs in question had that, then there needed to be a review for the info to be declassified.
However, if classified information needs to be given to someone without US clearance, such as a foreign military officer or political leader, the president can absolutely order that the information be provided and possibly downgraded. He can either authorize "disclosure", meaning the party can have access to the info -- like viewing a video of touring a facility; or, he can authorize dissemination of the information, in which case copies of documents, software, etc. can be given to the party.
Even Top Secret docs can be classified for reasons that are now OBE, and the former President still, as the OADR, has the authority to downgrade it.
If we are talking about missile launch codes and names of CIA agents in the field, the that's a bigger issue than declassifying something that were simply classified working papers.
The government has a habit of over-classifying most of what is classified, and failing to declassify when it's time to do so.
I'd like to see the specifics on what was deemed classified, and whether or not it was really a threat to national security by storing it in his home. If it was printed off a computer, by default it's labeled with a classification or special handling on each page until someone gets time to review it and possibly downgrade it. I had a ton of listings stamped with a security banner top/bottom-front/back of every page, The info they contained was actually unclassified, but the default markings were "SECRET" until two people in my office signed the front downgrading it.
We found it was more efficient time-wise and cost-wise to put them all in burn bags for classified destruction than having to go through literally tens of thousands of pages and mark out the headers.