Well sure, it doesn't appear that vos Savant was asked the Monty Hall problem. She seems to have been asked an ill formed alternative problem and answered that instead. Then the interpretation of the ill formed question with the most interesting assumptions about the host's behaviour became the Monty Hall Problem.
And the linked article (and by extension Mr. Diaconis & CrazyStat) was talking about the question that vos Savant was asked as opposed to the one where the assumptions to come to an answer are enumerated.
> We can safely assume, like Savant, that Monty always picks a door with a goat, turning this into a logic puzzle about probability.
No we can't. Otherwise we can safely assume any random axiom, like "The answer is always the 3rd door". You have to work with the problem as written.
And the linked article (and by extension Mr. Diaconis & CrazyStat) was talking about the question that vos Savant was asked as opposed to the one where the assumptions to come to an answer are enumerated.
> We can safely assume, like Savant, that Monty always picks a door with a goat, turning this into a logic puzzle about probability.
No we can't. Otherwise we can safely assume any random axiom, like "The answer is always the 3rd door". You have to work with the problem as written.