The IA isn't, but the argument was that copyright is dumb, not that a nonprofit like the IA should have exception. Archiving and making publicly available are different things though, so I don't think an exception for archiving should extend to distribution. The archiving also clashes with individual privacy rights and the "right to be forgotten" (which I'm not a big fan of in its depth, but totally agree with in principle).

Perhaps not having distinct terms isn't the worst thing: it reminds us that history is largely fictional, both on the personal and the society level, and its truthiness and usefulness is derived from our shared belief in it.