By your standard, if the child was born in the US to American parents but they moved, renounced their citizenship, and educated the child abroad, that child would be eligible.
The point was obviously about debating skills. Sarah Palin is very good at grandstanding while mouthing empty platitudes, but not much more. Her administration of both Wasilla and Alaska were nowhere near as conservative as touted. Ted Cruz on the other hand has shown himself to have a far more complete grasp on the application of interaction of legal, economic, and Constitutional principles with the historical knowledge to back them up. In a debate, he would crush her.
Stop projecting . You are beginning to sound like one of the lefties.