I don't think it's that simple; we could have out-competed them in a different way - perhaps by maturing faster (highly plausible given the relationship between extended childhoods and intelligence) so that we were better able to 'bounce back' after losing tribe members to conflicts, or by being able to adapt more easily to different types of terrain, allowing us to more easily survive poor weather and climate change. (If humanity were to be wiped out by a plague, would that imply that the relevant virus was smarter than we are?)