>> Crucially, for half of them he preceded his request with the superfluous apology: "I'm sorry about the rain!" The other half of the time he just came straight out with his request: "Can I borrow your cell phone?"

Couldn't it just be the chit-chat? I mean "Hey, how are you? Can I borrow your phone" versus "Can I borrow your phone", would probably give better results too :-/?