@Sjeng-
The NA Quest Book avoids things in another way. Apparently a change was made to get around those problems mentioned by you and el_flesh. The pertinent information states:
[description of how to place the tile]
...When a Hero attempts to leave this room, he must first roll 1 d6 to see which door he will use to exit.
If he rolls a 1 or 2, he exits through door 1. If he rolls a 3...If he rolls a 6, he exits through door 4.
The part about monsters not entering the room was entirely omitted. I think it is also more clear how a Hero leaves the tile.
As for the EU Quest Book, I agree with Goblin-King on how to play the door and envision its workings. The "any exit" applies to the intended outer exit, which at that time the inner door apparently lines up with. The problem is, the confusing nature of the room likely will place the Heroes elswhere, randomly and actually deciding "by which door they leave." Your last post pretty much states the same.
My personal preference would be for the a door to shut after a Hero exits. There wouldn't be a need for magical confusion that way. If I ever play this one again, I'm going to add auto-shut doors to the mix. And perhaps some lute elevator music.