Here is how I think this stovepipe compartment worked.
The archives bring over copies of what they have.
The committee thinks they have good docs.
Berger goes in and is supposed to pick out what the committee might want to review. Berger substitutes a fixed copy, gives that to the committee, as one he picks out.
The committee thinks they have good copy, nobody is the wiser. Until Berger gets caught smuggling something out. Watergate take two HA .
It would be laborious to go back to the archive and get another copy. No one would probably think to do this. Or they could have had the original and Berger was actually revising it.
The process is usually serial, with only limited people in the room at a time. But since we don't know how they were running the room, it's just my educated guess.