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You are correct, when shuffled all cards reset and go back to their owners (unless it says for remainder of game)
they would be unusable then
Any card, when about to go to any deck or discard pile, goes to its owner's pile instead.
JSB is correct and here's just a bit of an explanation. When writing special abilities, we (the playtesters) try to keep the amount of necessary text to a minimum so that card art can be fully appreciated. One example is that whenever a card says "deck" the default meaning is "owner's deck."