The usual use of the phrase in a sentence seems to be as a sort of passive-aggressive verbal punctuation mark in a case where the person does know what he or she is about to say. The example he gave that seems to me to be THE example of this tendency is when Liz got her learner's permit and wanted to get in some practice behind the wheel. Elly's response was to whip out the phrase "I don't know" before stating why she DID know that Liz would be standing at the curb watching everyone else but her drive. It seems to me that what Elly meant to say is that "You should probably have realized that your father and I still need to drive to work and Michael has to have wheels so, no, you can't drive because we've only got two cars" but felt that the phrase softened the blow.
The secondary use of this is to refute someone's statement. The best case of this was when John used to to tell Elly that he felt closer to Liz emotionally than he had ever been before when the two of them had got to talking long-distance. She might have been three cassette tapes away by car but making an emotional connection made her feel as if she were across the table from him. His use of the phrase is thus short for "I believe you're wrong about the distance being a problem" cushioned by a feigned ignorance.
Finally, we come to its literal use when a Patterson does something he or she really doesn't like to do. This, I should think, is what they have in common with Red Green: a dislike of expressing confusion or ignorance. A Patterson doesn't like to look stupid because of a beloved logical fallacy so this is not a use of the phrase they like owing to it leading them to fearing that the person spoken to will wonder what else they don't know.