I guess Bolivia
This is from the trivia section but the writer never explains these three clues.
"Although great pains were used to disguise the name of the country in the film, Dr. Ferguson mentions that Pres. Farrago should go to a neurological hospital (which he mentions is just across the border) in Chile - which narrows the country down to either Argentina, Bolivia, or Peru. Other hints include: Peso/Dollar law, the blankets worn on the train, license plates on vehicles."
Peru did not have the peso as a currency. Early on they mentioned going back to the boat so that would rule out land-locked Bolivia as their origin point. The guitar player sounded tango-ey so that could be Buenos Aires. But there was that long train ride with mountain scenery to deliver the doctor to the capital. My guess is they were kidnapped in either Argentina or Chile and taken to Bolivia.
I know there are problems with this guess but I'm trying to solicit some more clues/guesses here.