I'm pretty sure the rule book says something along the lines of "unless otherwise stated, all cards drawn or discarded from the deck are drawn or discarded from the top."
And seriously, think for just 30 seconds. This is a game where you don't need to interact during your opponent's turn. Why the hell are they going to make you pick up your deck and search through the entire thing to find that one card you don't mind discarding during your opponent's turn?
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