They're just trying to recreate the whole vigilante, dark protector persona that was Sting when he was at his most popular in WCW. Back then, the New World Order threatened the very foundation and tradition that WCW stood for, and now, he sees The Authority as an almost equally oppressive, power-hungry force that he knows needs to be stopped before it becomes too big to do anything about.
As for referencing anything from the past, Triple H has been knocking Sting in those sit-down wwe.com interviews with Michael Cole, saying that the reason he never came to WWE before is likely because he was afraid of having to step in the ring with him (HHH.) Given that this would be around the time that HHH's "reign of terror" title reign would have been, they can even have Hunter reference how beating the best of what WCW had to offer (Bill Goldberg, Scott Steiner, Booker T., even his good buddy Kevin Nash) must have scared Sting away.
It'd also be epic to see them unabashedly try to recreate one of the GOAT WCW moments:
Just have former NWO members Hall, Nash, and X-Pac (a nice nod to the old Sting vs NWO days, and guys they've already established as Hunter's buddies on-screen) team with Kane, Big Show (heh, another former member of the NWO), and maybe Rollins one night to gang up and attack Sting, and then have Sting appear out of nowhere and have him start whooping their ass with a bat. He then calls Triple H in the ring and they have a brief physical interaction just as Sting and Hogan did in the video. Just replace Dennis Rodman warming Hogan up with Stephanie yelling "Get him!" to Hunter or something. Maybe this could be what goes down at Fast Lane.
