[mannykannot]

This is a fairly common reacton to the puzzle these days.

In the time and place of the problem's first widely-distributed posing (Parade Magazine, 1990) it might reasonably be assumed that many people seeing it there were somewhat familiar with the game show it is loosely based on.

Even without that background, one might reasonably deduce that the second door opening never reveals the prize, as there would be no point, in that case, in asking whether the contestant wants to change her pick.

That is a somewhat meta argument, in that it involves understanding human intent and what makes for a good puzzle, and it means that it is not just a math/logic/probability challenge, but it is nevertheless a good puzzle. There's no law that says a puzzle must explicitly state every fact of the matter.