The problem with the Monty Hall problem is that it is rarely, if ever, correctly stated, because to state it correctly is to give away the game. Thus, the "statement" of the problem in the article says:

Mr. Monty then shows you the goat hiding behind one of the doors that you DID NOT pick.

But in the analysis of the problem, we have:

Monty Hall exposes a goat no matter which door you choose to enter.

These are very different conditions. In the statement of the problem, we are not told how Monty came to open the door he opened. Must Monty open another door at all? Maybe he only opens a door if the contestant has chosen the door with the car. If the guy has already chosen a goat, maybe Monty would offer him money. Does Monty know what's behind the doors, or does he open one at random? Can we argue from the facts of TV life that, for the game show to be interesting, Monty must know where the car is and must open a door with a goat? Maybe, but for the 2/3-1/3 logic to apply, Monty must, no matter what, open a door that he knows hides a goat, and the contestant must know that Monty is bound by that rule. Otherwise, the player has insufficient information to solve the problem.

If we state the problem with all of the necessary details, it doesn't "work" as a brain-teaser, because it's too legalistic. But without the legalisms, it doesn't have a necessary answer.