I'm sure there's some truth to that, in situations where the choice was made using some basis for making the decision. But since in this situation they are assuming you have no basis for making the original decision (each box is equally likely to have the keys), it's hard to imagine how the first ...
It's still the same game, just now you know the opened box does not have the keys in it. The odds are still 1:3 that the box you picked is the one with the keys in it. But now it's 2:3 that the unopened box you didn't pick has the keys. Only if after opening the third box did the game show host ...
Hopefully I am not spoiling Fingers' puzzle by posting this hint. In this puzzle, N =3 (there are three boxes). It's easier to see why the answer is what it is when you increase N , say to 1,000,000. The keys are in one of a milion boxes, and you pick one, then the game show host opens all but one ...