Unfortunately for your beliefs, Diamond confirms the dependency thesis, not your independency belief. The advantages luck granted Europeans were used for plunder and slavery and wealth extraction from the "new world." This greatly magnified the disadvantages of what consequently became the Third World and the advantages of the First World. The fact that Potosi's silver was carted off to Europe, and Potosi's laborers were enslaved and entombed in her mines, along with later repetitions of the same basic capital-draining process, explains a large part of the results in both worlds.
Astounding you could read Diamond and miss out on the fact that this is precisely his argument! The Third World has always been trapped in an unfair system bequeathed to the G7 elites by chance, and enforced by their greed and brutality.
Diamond's thesis on civilizations' decline is that out-of-touch and unchecked ruling classes are the key social determinant of that process. How sad to hear folks on this board spouting one of the core ideologies of our unchecked overclass -- "Third World, heal thyself!"