HBOIt's doubtful that Rust would seek the Throne for himself, but he would not be fooled by anyone's duplicitous nature for a second. Ned Stark made the mistake of believing that people in Kings Landing still had honor like him. Rust understands the true nature of people. He would have known nobody in Kings Landing would stand against the Lannisters even if he outed Joffrey's true parentage to the world. He would have kept the information to himself until he knew how to use it and would never have trusted Littlefinger, Varys, or even Renly. Rust would have found a way to have Joffrey removed from the Iron Throne (one way or another) and would have done everything to make sure that all the liars and corrupt officials got their comeuppance. Unfortunately Rust would probably draw a lot of attention to himself, asking so many questions, and his cocky, disinterested demeanor would probably irritate the people in charge who couldn't intimidate him. Rust would make a lot of enemies, and have a target on his back, but he would expect it. He would know how to survive. He wouldn't want the Throne, nor would he be particularly interested in who won it, but he would do whatever it took to make sure whoever takes the Throne deserves it.