Comment I don't see a problem unless they use a certain HD (Score 1) 88
...and why should it be?
Whoever wants to keep the originals can - at their own expense or by fundraising. This means that those of historical importance will be kept and paid for by the government (ultimately us then).
The digital copies should be held in a primary location on secure and unalterable media (yaay, bring PROMs back - what capacity would they be now?) and also on other widely separated sites as backups.
When a document is requested from the primary site it can be comparatively authenticated from multiple sites.
Regular comparative audits can be used to check storage integrity, any anomalies would be either tampering or hardware failure and a trace would sort out which and indicate what action to take.
TL:DR - the government sticks everything in a 4MB DX2-66 box running DOS 4 and Telnet with everything on a crate of old Deathstars found in a closet. You know how it ends.