Thanks for sharing. It is akin to what I've noticed before too. How do BA sort it out when someone actually slips by? Do it for them in the airline office in EZE?

There is no "slip by" involved when the US citizen with a US passport has Argentina as the listed place of birth or an Argentine birth certificate. Such US citizens are being admitted into Argentina by Argentine authorities without being required to pay the reciprocity fee. That is why I questioned the claim about "slip by".