This is an awkward interview. I think the bottom line is this. Williams says that he embellished stories to enhance his role in certain events he was involved in (kind of like a fisherman would exaggerate his exploits). This started not as a part of his news reports but in interviews and conversations outside of his reporting. In his own mind over the years, his exaggerations took on a life of their own–so much so that he was no longer distinguishing fact from fiction in his own thinking. He apparently began to believe his own fictions and repeated them years after the fact, not recalling (perhaps not choosing to recall?) that they were not true.
Like I said, this conversation is awkward. But there is something deeply revealing about human nature in all of this. Even our memories are morally implicated by sin. People tend to remember themselves as the hero of our their own stories. They recall (and sometimes invent!) what buttresses their self-image and suppress what does not. These fictional accounts of ourselves tend to emerge rather spontaneously from our nature as sinners (Rom. 1:18). People can be easily, happily, and even obliviously self-deluded.
You can watch the interview above for yourself and judge for yourself whether I have the correct read on this. Or you can read the report here. You can read Albert Mohler’s comments from last February here.