I believe Volition turn it to over the top silliness is to avoid people keep comparing it with GTA or calling it a GTA clone. Saints Row started out as a GTA clone and now it is more like a class of its own, mainly you cant get funny weapons and ridiculous jokes in GTA.
Well, if you look at the classic GTA3 series (GTA3, GTA:VC, and GTA:SA) there was some good of amount of silliness. Sometimes even the eccentric situations that the protagonists get into surprise the protagonists themselves.