Well in anticipation of our visit to Mt. Rushmore on the Long Ride to Sturgis, I did some research. Here is what I found.
Secret Chamber at Mt. Rushmore: True -- There is a 50-foot tunnel in a
crevice behind Mt. Rushmore that was originally envisioned as a "Hall of
Records" where copies of important United States documents and other
artifacts were to be stored. The hall was never completed as envisioned;
however the tunnel exists and a small cache of records was placed in a
scaled-down version of the Hall in 1998 through the work of the Mt.
Rushmore Historical Society. It is not open to the public
Unexplored Caves: True -- The Black Hills has many unexplored caves and even most of the commercial caves and those in the national parks have not been fully explored.
SO THERE YOU HAVE IT!