Conspiracy theory time!
Maybe Stern and Sterling are actually super secret friends. And Sterling told Stern to shoot this down, so Sterling could tell Paul that he doesn't have any blood on his hands, in the hopes of tricking Paul into staying anyways. I really don't think Sterling wants to pay Doc.
I mean, Stern helped Sterling get Paul in the first place.
Come on, this is at least as believable as Stern rigging the lottery, right?