TBH there is more than one vault. Usually when they talk about "The Vault" they are talking about a series of large rooms carved out of solid granite in one of the canyons. (Same granite deposit that was used in the building of the Temple). Space in this vault is rented for the off-site storage of back-up tapes from all over the world.
In the Church administration building there is also one, (or more), "vaults" which contain archives and items of importance in church history. These vaults are closed to the public, but may be connected by the tunnel network.
The tunnels have been there for years and are well known by Mormon faithful. The tunnels allow church leadership to move between headquarters and the temple and other buildings without being exposed to the press or elements.
If they would answer their robo-calls they could still get the extended warranty...