Edit: looking in the background, you see the vault door. I guess you pick it up before you leave. Never mind, thought too hard. You can lock/delete this thread.
From the looks of the video where you find the Pipboy, it looks like you find it when you are leaving the Vault, not already outside of it though. You probably just find it on a corpse who couldn't get all the way inside of the Vault before the door closed.
My theory is this...The elevator we rise out of is not the vault door itself. It's just an elevator down to a cave that leads to the vault door.
The area we find the Pipboy looks like a platform, underground. I'm thinking once we emerge from the Vault, when we leave the actual vault, not the elevator, that's where we find it.
The Vault door looks like a standard vault door so it is possible that the elevator is part of some weird airlock.
I've toyed with the idea that this is how Vault's are this time around, instead of being found in little caves, they're buried with the elevators.
Its all speculation? All we have seen is bits and pieces...will have to wait till nov 10?