Cutaway Gags are commonly used in all Family Guy episodes and normally do not have anything to do with the storyline. They are used after a sentence or conversation, usually starting with "This is even worse/better than the time..." and are the comedy part of Family Guy.
It is implied that these gags are simply stories made up by the people that set up the gag, and that the incidents shown did not really happen. This is particularly obvious when it comes to parodies of movies and television shows, or incidents that show a character dying.