If you read my post on the API system, you would see that the problem isn't filling out a form or just being randomly asked about it by the immigration agent. The API system, which EZE now uses, tells the destination country about your conviction as you are on the way there. So the immigration agent doesn't need to ask, they already know.
So worst case scenario: you get on your flight in the US. No problem, you don't need a visa to visit here. You have a valid US passport, the United Sates doesn't care that you're leaving. Whatever airline you are flying sends the passenger information, which includes any criminal history, to immigration at EZE. Your offense is one that Argentina has a problem with, ie a potential sentence of 3 years or more. As you get off the plane, officials are there to greet you. They take you into an office and explain that due to the nature of your conviction, you are not allowed to enter the country. They put you on the next plane out returning to anywhere in the US.
That's why, to be sure you can get here, it would be best to research which neighboring countries don't use API yet and then make a land/boat border crossing.
So worst case scenario: you get on your flight in the US. No problem, you don't need a visa to visit here. You have a valid US passport, the United Sates doesn't care that you're leaving. Whatever airline you are flying sends the passenger information, which includes any criminal history, to immigration at EZE. Your offense is one that Argentina has a problem with, ie a potential sentence of 3 years or more. As you get off the plane, officials are there to greet you. They take you into an office and explain that due to the nature of your conviction, you are not allowed to enter the country. They put you on the next plane out returning to anywhere in the US.
That's why, to be sure you can get here, it would be best to research which neighboring countries don't use API yet and then make a land/boat border crossing.
