So what's the clarification then? It is not a mistake to show your US passport if you intend on traveling on it and want to travel as a US citizen.
Most people who live in the US traveling for under 90 days with a US passport will want to present that to enter Argentina because they will have to return to the US on the same passport and it makes sense and is easier to do all travel on one passport.
According to those DNM links, if you are from a country that doesn't have a dual nationality treaty with Argentina, they will give you 180 days. So it sounds like the guy just erroneously applied this procedure to the US passport entering.
Since there is a dual citizenship convention with the US, they should treat Argentine-born people traveling on a US passport as US citizens and only give them 90 days.