United will definitely give you trouble- I just had that experience with them. After a long argument and almost having to buy a $2000 refundable ticket someone wandered out from the back with the rule book and it turned out that they only had to "advise" people that they should have proof of onward travel, not require it. But it was a pain in the ass and it's easier to just get a cheap bus/boat ticket out of the country. I ask and they said they would accept that.
Argentina doesn't care at all, like others I have flown in several times with no proof of onward travel and have NEVER been asked to show anything. It's just the airlines.