Your memory changes every time you tell a story.
Police have to be very careful when questioning witnesses. They basically treat a witness's memory like a crime scene: once you go over it a single time, it's irreversibly disturbed. For example, asking a biased question, even unintentionally, can make a witness tell their story a little differently. Doing so doesn't just change the story; it changes the witness's memory, permanently and irreversibly. And this isn't just true of witnesses. The more we tell stories, the more our memories change.
There's a basic recipe for making a false memory: imagine a scene in vivid detail, do so repeatedly, and believe that what you're imagining is real. Consider again Mike Daisey's supposed conversation in English with a 13-year-old girl. He has surely replayed this incident in his memory dozens or hundreds of times. He surely remembers it each time in detail. Even if it never happened, this would make it seem completely real to him. And of course it's in English—his imagination speaks English, not Mandarin Chinese. What he's really remembering, each time he tells the story, is whatever he remembered the last time he told the story. His translator may have rehearsed less, but her memory is also less warped.
I personally try to be careful about remembering stories too often, because I know they're subject to change. I know the second time I tell a story, what I'm remembering is the first time I told the story. And the 201st time, I'm really remembering the 200th time. Many of our memories are records of our own stories, not of events that actually took place.