My understanding is that the term arose from the existing body of international law, in which case "natural born" would mean only that the birth was from parents who were both citizens (for the reason you state, to preclude any foreign obligation by birth). The requirement on ordinary citizenship is either (a) birth in the United States or its territories, or (b) birth wherein one or both parents are citizens. My cousin was born in France of an American mother and a French father and has both American citizenship and French citizenship.