It was my understanding that Bret's WWF contract didn't expire until a few weeks after Survivor Series. Bret agreed to lose the title before his contract expired, but Vince was afraid Bischoff would announce on Nitro he signed Bret before his WCW contract kicked in. Not wanting to face the embarrassment of WCW announcing they signed the current WWF champion, Vince felt he needed to get the belt off Bret ASAP. And the night after the screw job, Bischoff did announce he signed Bret Hart, while he was still under contract to WWF.
Correct me if any of that is wrong.