The airline is supposed to make sure that the person is in compliance with the immigration laws of the country. If you have a residence visa, then there's no problem. Otherwise, you are supposed to show that you will not overstay the length of the tourist visa. If you can't, the airline can refuse to check you in until you get one. The explanation I have heard (unofficial) is that if the person is refused entry to the country for not appearing to comply with the immigration laws (ie, for appearing to plan to stay indefinitely on a tourist visa), then the airline gets stuck with the cost of flying the person back home.
Whether they enforce that rule or not depends on the airline. A year or so ago a friend of mine who owned an apartment here was not allowed to return to Argentina (he was flying back from a visit to the States) until he bought a return ticket. He got a fully refundable ticket which he later cancelled (although he still got stuck with a fee for having bought the ticket at the counter). The airline in that case was Delta.
I never had any issues, but I always have to show my DNI (as well as my passport) when I check in at EZE. I think the airline then makes a note that I am a permanent resident, so there is never a problem on the return flight.