Mission:Possible - Door to desktop (bear with me)

Okay, so I'm watching the original Tom Cruise remake of Mission:Impossible, and it gets to that very famous scene where Cruise is hanging from the air conditioning duct and can't make the temperature go up, or make a sound or touch the floor or the security system goes off and he's toast. As he's doing this (catching his sweat drop along the way), he's logging into the single most important CIA computer mainframe (do they still call them that? Mainframes?) with the password that he got from the guy who normally mans that ultra-secure room (who's in the bathroom because they poisoned him just a little). This is all very exciting, but the whole time all I can think is: Jeez, how hard is it to link the security system to the computer network so that it knows that the network can't be accessed by a person who hasn't just keyed in the door? Of course, the movie was made in 1996, and Tom Cruise emails people through a little program that shows him a digitized post card with a digitized stamp, but it really doesn't seem like it should have been that difficult even back then. It really blows my mind how late IP communication came to security.