DNI is of no use in the Airports.
Travelling in brazil and rest of south America, I only travel with DNI inside south America (Brazil, Peru, Bolivia, Chile, not sure about Colombia and Ecuador) and that is the only legal requirement as argentine, now I don’t know what happen with DNI if you have a temporal residency in Argentina or if you are not Argentine, I never saw a DNI for foreigner so I don’t know if there is a special mark on it saying that you are not Argentinean.
The DNI with permanent residency is not same as the DNI of a naturalized citizen. Lets say if you were born in Nigeria and you have a DNI but marked as a Nigerian citizen..you must carry your passport with the visa of Chile to enter Chile and so on and so forth.
Regarding entering Colombia, Peru, Venezuela - I am always asked for my passport ( Argentine) ; DNI was not accepted. But for Brazil, Chile. Uruguay, Paraguay - DNI is more than enough if you are Argentine. Never went to Bolivia. Its also ironical that the immigration of Peru, Colombia and Venezuela always asks many questions and stamp 15-20 days only entry in the passport..if you say..you are here for a week. Unlike Brazil, Uruguay, Chile etc..where no limit of stay is stamped. Its ironical cos Argentina is full of Colombians, Peruvians and now Venezuelans looking for immigration.