We have an account with Banco Frances with temporary DNI's. We actually first opened it with our passports, before we had DNI's. We have several Argentine credit cards which some people say only Argentines can have. There is a lot of confusing information out there, and it depends on the bank, and the time of day, and what the weather is like, and whether it is an even or an odd day, etc etc. Perhaps the fact that my husband is employed by the CONICET as a monotributista helps, no idea. On the other hand, I have a friend who is a permatourist and has a bank account with Banco de la Nacion. All he needed is a CDI which anybody can get.
Yes we are talking caja de ahorros.