Some additional problems that might show up, at least it did to me (pseudo-tourist, no DNI, yet). Though Delta was happy to sell me a ticket EZE-AMS-EZE (via Atlanta, return departure from Brussels, which was about $300 less), they refused me onto the plane back in Brussels. They said I needed proof of Argentine citizenship or residency, else they could not let me on the plane, being afraid I would sent back at EZE, which might be on their planes.
I told them that I planned to leave over land (which I normally do and have dozens of stamps to prove it, we live 50km from Chile), but to no avail. I also asked them why they sold me a return ticket from/to Argentina if I could not use it, but no.
One helpful man at the Delta counter tried to help out by selling me a 100% refundable Delta ticket back to AMS/BRU, which I could then supposedly have canceled after having landed. The costs was so high (over $3500), that my Credit card could not handle it and I did not have enough cash. It took over 30 minutes to find a solution while the plane finished boarding.
In the end I managed to get quickly to a travel agency at the airport and get a one-way ticket BA- Montevideo, which was the cheapest flight out of the country in the next 3 months (still about $200 I think. With that useless paper, I was let on. No more Delta, I had no problems before, but will avoid them.
Just FYI, might be good to have some proof of living in AR with you when boarding abroad.