Cooke says that the actual Declaration of Independence and Constitution aren't on display, but are actually in Fort Knox. This is not correct as they are on display at the National Archives in DC. From 1941-1944 after Pearl Harbor these documents were stored at Fort Knox.
Cabe and Tim say they are off the base, then after Walter, Toby, and Happy meet Cooke they are then back on the base. While it's not impossible they re-entered the base, it is unlikely since there is a full-blown security issue going on because of the break-in. It may have been open that the water tank they escaped from was on the base except that Cooke is then caught while attempting to leave the base indicating the tank is within the base. The entirety of the depository is within the military base.
Walter is shown getting access to the vault with a swipe card taken from a guard. Entry into the vaults actually follows the two-man rule where no one person has security access to gain entry alone.