I was assuming that running, say, 100 trials meant going all the way through a 100-card deck without shuffling.

I believe this should be the case. There's no need to reshuffle between each trial because it would unnecessarily complicate things. I'd assume they reshuffled a deck of hundred cards after every 100 trials.

Also, if you put the card back and reshuffle, you cannot guarantee a %70 success rate as described.