I think they used to have to do it when they had a video category 'cuz they had to run the clips sequentially.
Proof and therefore real: There was a video category in my game, and we were told during the break that for that category, and that category only, the clues had to be taken in order. We could, of course, jump away from the category and later back to it, but still in sequence.
But no, I don't remember such a rule in the Fleming game Such a rule would make a bit of sense, since the cards were being pulled manually. Of course, I also don't remember an out-of-order pick on he Fleming show either.