They don't need history if the storyline's set up right.
HHH continues to try and screw D-Bry and others who the fans back, starts to get out of control. Vince makes an appearance on Raw and announces that either he or the WWE Board of Directors is starting to question the judgment of HHH/Steph/Kane/The Authority and the decision has been made to put somebody in a position to counter their power. He then talks about somebody with a long history in the sports entertainment business, a man who has held numerous titles and who owes nothing to HHH, the WWE, or anybody else...except the fans. Then he reveals that Sting (who appears sans makeup, in a suit, MEM-style) is the man that he or the Board has chosen to do that. (Titles don't matter; they'll give him one.)
Hence, no history between Sting and HHH is necessary. Sting is a known commodity by WWE fans (they voted the guy the best US Champion of all time, after all) and he's been a face for most of his career. Further, he's generally considered one of the best natural faces in the business while HHH is considered one of the best natural heels in the business. Their confrontations would be classic.
(By the way, I know that won't be the wording of a Vince-brings-Sting-to-WWE promo, but Vince has good instincts and knows how to cut a promo, so I'm not too worried about what he actually says. It'll work, whatever it is.)
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