I believe the rules lie with your nationality e.g. if your nationality is Argentine (and other Mercosur or other neighboring countries that have an agreement with one another for freedom of movement within the region), you can go to Brazil with only your DNI but if you are a foreign national with only a DNI (be it temporary or permanent), you need your passport. My case for example, I have a DNI (permanent residency) but my nationality requires a visa for Uruguay, so I can't visit Uruguay with my DNI. Instead, I need to apply for the visa before going to Uruguay.