The fact that that the 2 of hearts *has* to be in its correct place if both the 3 & 4 of hearts are in their correct places doesn't warrant any special consideration ... that I can see, anyway.

I was with you until that last sentence, which I don't get. There is a difference between sampling with replacement and sampling without replacement. I would argue that checking all of the cards in the deck, instead of just one, is sampling without replacement: Once the position of the first card has been checked, there are only 51 cards in 51 possible positions remaining, and so on.