The easiest way to answer that question is to quote PC himself. He was asked that question way back on the old (now closed) official PC Forum. There were Q&A sessions. Users could ask questions, the list was passed on to PC and his replies were posted on the forum some time later. This must have been around the FFF Tour.
Here is what he answered regarding the introduction you mentioned:
Quote from Phil Collins Q&AI've used this in many intros, and it comes from a Steve Martin sketch when he says that and does something outrageous. His stand up comedy was a huge influence on me in the early days. I considered him to be my "private find"... I didn't realise he was so huge in America !!! A lot of the Genesis intros, and my own solo tour intros were steals from him. I feel both guilty and embarrassed by it now.... but hey !! I was young.....
Hope that helped.