Let me reiterate what I have already said. If you consider that this game is one of a series of games (i.e. this game is played daily), then the outcome is different then if you consider that the game only happens once. If you consider this scenario as one of a series then it becomes a question of economics more than purely math. Economically you should assume that the show wants to maximize profits and therefore minimize costs. If it is possible for the chance of receiving a car to be 1/2, then the show will make the probability 1/2.

As I stated before it is possible to make the probability of winning by switching to be 1/2 if Monty sometimes opens up all the doors without giving the contestant a chance to switch. And if you've watched "Let's Make a Deal" you'll see that he does in fact do this. Sometimes the contestant is given a chance to switch and sometimes he reveals what they get after just one pick. The show very much has an air of unpredictability. You don't really know what Monty is going to do next.

The only real way to know if the producers are playing some metagame or not is to actually observe how often the game is played in this fashion and record if the observed probability is closer to 2/3 or 1/2 (or perhaps it is close to neither). If the observed probability is close to 2/3 then we can assume there is no metagame, otherwise we must assume that the producers are somehow affecting the probabilities of the game.