_However_, they have to operate under the same BS everyone else does, so it seems naïve for them to take reckless actions that could put them in this position
As a nonprofit and public archive/library they do have some special rights, which is why this isn't as clear cut as many think. These range from codified in law https://www.copyright.gov/title17/92chap1.html#108 to US Copyright Office decisions like https://www.copyright.gov/1201/2021/ and precedent.
If you did this you'd be sued into the ground and 100% lose. Now, I'm not saying the Archive will get away with what they did or that it was a good idea, just that there might be some non-obvious avenues.