As always, South American rules are not very clear, but it seems that indeed CONMEBOL organizes the competition, as I have verified on their official website: "oficializada en junio de este año por la Conmebol", but actually I don't know if CONMEBOL puts the restriction or not. Anyway the rule about the restriction is published on their website: "Las principales figuras del futbol que jueguen en la liga local de ambos países, formarán parte de sus respectivas selecciones. También podrán ser convocados jugadores argentinos que militen en Brasil y jugadores brasileños que lo hagan en Argentina."
I have discovered another curious issue: also in Africa, CAF organizes an official competition called African Championship of Nations, where only the local players can represent the National teams. Two editions of this tournament have been played so far: in 2009 and in 2011. But the matches of the African Championship of Nations are not on FIFA's list...
Yes, it's not clear with the CHAN (African) competition. For the smaller nations (like Djibouti/Somalia), their local-=based team is exactly the same as their national team. But for the big nations (Cameroon, Côte d'Ivoire), it is a completely different team without all their European stars.
But, it can also be said that the CECAFA and COSAFA cups are also mostly for local-based players, BUT these matches are counted as full internationals. The Amílcar Cabral Cup (North-West Africa) was also mostly for local-based players. Also, the Indian Ocean Island Games is basically for local-based players, as not many players from these islands play outside Africa.
But the difference is - there is no restriction in place. IF these countries choose to play European-based players, there would be no problem. However, in the CHAN tournaments of 2009 and 2011, it was forbidden to play any players from outside Africa.
About Argentina v Brazil - I am not sure if CONMEBOL put the restrictions on the players - if so, then the matches should not count. However, Argentina has played a few friendly matches in the last few years with a local-based "B" team, as they chose to play on non-FIFA dates.