Sorry, your attempt to make a comparison by using the King of Jordan (or Churchill) FAILS as both lost their citizenship when they joined as an officer of a foreign military per USC Title 8 Section 1481.
AGAIN: You conveniently forgot that the 1790 Naturalization Act was completely rescinded, and any mention, ever, by Congress, of natural born citizens was replaced by “citizens”.
You open Pandora’s Box~
So you claim all the little bastard offspring milling about SE Asia that are the result of American men abusing sex-tourism are eligible. And you will soon have the jihadi ISIS sons of American brides that elope to the ME. eligible as well.