The Greenbrier Bunker.
Most likely this is what they are referring to.
‘50s tech no longer a secret.
The Greenbrier bunker was a real thing—they offer tours these days:
https://www.greenbrier.com/activities/bunker-tours/
The nuclear bunker was a dubious proposition even then—the logistics of getting people there before nuclear weapons hit were highly questionable.
Today it would be ridiculous—just a few minutes before a sub launch from the Atlantic to Eastern Seaboard targets.
In the case of an Eastern seaboard decapitation strike there are known bunkers in the west for continuity of government.
The NORAD Colorado site is one and supposedly there is one in Omaha as well.
I attended a couple of industry meetings at the Greenbrier in the 1970s.
At the opening dinner the manager of the Greenbrier welcomed the delegates. His first remark: “Welcome to the poverty-striken hills of West Virginia.”