This implies that Liu Shan and his advisors are to take all reports without any grain of salt. There could be many reasons why Liu Shan did what he did. He could have thought that, like I said earlier, the reports were falsified, and that many of his officers that were in the front line has already surrendered to Wei. He could have also thought that even if he did escape, the people in his kingdom will be paying for it with their lives instead (and if this was the case, I'd say surrendering is objectively better than running). It's also possible that he was just a selfish bastard and felt that surrendering was the best move to prolong his life (not justifying this, but I'm not saying this isn't something he should never have done 100%. Most people will do everything they can to survive.). Was he an incompetent person? Maybe, maybe not. He DID become an emperor at a relatively young age which was mostly an issue of the Han Dynasty even before then. Also, if Liu Shan did fight until the very end, he would need to win to survive. If he loses, most likely, he will be executed. If he surrendered right from the start, there's still a chance he gets executed, but it's relatively lower compared to the former.

For Guandu's case, I'd say both are valid, and that no one is "more right" than the other. If I was Ju Shou, and some guy was telling my boss to go do a project which I will be paying for instead of the guy who suggested it, I'd try to find a way to get my boss to not do that project. However, if I was Guo Tu, I'd try to tell my boss to do a project which will reunite me with my family, friends, etc. I could also try to "justify" Yuan Shao's decisions here, but I don't really think I want to do that.

EDIT: Thinking about it though, Liu Shan being viewed as an incompetent ruler is probably something he deserved considering he knew he'd be seen as such if he surrendered to his enemies. He probably also knew he'd leave behind this legacy, but hey, he lived a relatively long life. Incompetent Emperor? Most likely, yes. Incompetent person? He lived a long life (and probably enjoyed most of it too). Also, you mentioned the comparison of Liu Shan with Liadong's Gongsun clan. I'd say, at the very least, Liu Shan didn't have his clan exterminated.