There WERE copy machines back then; and, one could never grab originals from the documentation center. Patrons were never allowed "in the stacks". Copies were brought out to you. I know this to be the case since I worked at the Marshall Space Flight Center in 1973+.
Anything that was lost was due to government and corporate destruction of documents in order to regain storage space. The scientists and engineers took nothing away except knowledge and technique.
But, as we see with Space-X, younger engineers are fully capable of going through the entire process the second time.
Well, the Apollo program ended in 1972.
You are right that some documents, telemetry, and video footage were lost due to government incompetence...sorry, to "regain storage space", though.