Here is a user-submitted recording of that segment from You Tube:
And here is a segment about the phenomenon from BBC TWO (this one is easier to view and I think it does a better job demonstrating and explaining what is happening):
The gist of the McGurk effect is that when a person's eyes see something different than what the ears hear, visual perception frequently overrules auditory perception. In other words, sight tells a person what to hear even if it is incorrect.
While not exactly the same, this reminded me of a gag children used to play when I was in elementary school. Person A would mouth the words "olive juice" to Person B. Thus, Person B would think that Person A had said "I love you".