Yes, they 100% do bring out unique archival records for you to review. It's one of the neat things about going to the facility!
Sometimes if there's a more extensive process to retrieve the record (i.e. your archivist has to talk to a different government entity or agency to get the information) you might get some facsimiles, but often the information is only captured in the physical document that you're looking at. Moreover, to reiterate my point from above, part of the reason that College Park is making this decision (probably) is because it takes time and coordination to get these documents, and they want to ensure that--with limited staff and resources--they're still able to fulfill their mission of providing access to information.
Most of the records that exist under NARA's purview are not backed up at all. There's a major initiative to digitize existing holdings, but that's challenging/fraught with staffing issues. It's basically an under- or un-funded mandate.
If you're interested, there's been a fair amount of theft throughout the history of the agency, and they actually maintain a page on it: https://www.archives.gov/research/recover/notable-thefts.htm...