The article is rather sparse on technical details. The homepage for LOCKSS is
http://www.lockss.org/lockss/Home.
It appears to use some sort of Byzantine fault tolerance in its auditing system (to detect the fault and repair) spread across many "boxes" running the system. There is also a manual audit process by librarians to check that content is correct (this may handle cases where the "live" copies are tampered).
For the most part (from what I can gather from their site), the system is a kind of "self-audited" backup for live content, not for ensuring that that live content is correct. So, for a document that you needed to keep correct (given that a live copy may be tampered), you could simply not have a live copy.