He's making a joke, not supporting his dissertation. He's allowed to be fast and loose with ideas for a laugh, as a professional comedian.
Do you think when he says things like "Takes the cake. Ya know, say 'Boy he really takes the cake'...Where? Where do ya take a cake? to the movies?" That he's exposing his own ignorance of idioms?
Yes, he's making a joke. It's funny and a pithy remark. The point is made. I find it an interesting point because when mocking other peoples' intelligence one ought to make certain they are correct. Sort of how when one criticizes another person's grammar they should make sure they didn't make a grammar mistake too.
Do you think when he says things like "Takes the cake. Ya know, say 'Boy he really takes the cake'...Where? Where do ya take a cake? to the movies?" That he's exposing his own ignorance of idioms?