Aden pre 30 Nov '67 wasn't Yemen. It was a British Protectorate (I think, if not still part of the Empire) so I guess if you were the child of the "Occupying Forces" you'd be British Citizen.
Yes...and no. Speaking as a forces brat born outside of the UK, I concur with Ian16th who notes that the US authorities invariably regard place of birth and nationality as the same thing (and it's up to you to prove otherwise). Also, even though I am British (born to UK parents in a UK hospital in a UK-administered territory) I have the dual-nationality of that other country on account of being born there.