Nothing in Argentina necessarily works the same way twice in a row-
BUT-
2 weeks ago my wife successfully opened a bank account WITHOUT a DNI.
She was told the only bank that will open an account for an extranero without a DNI is Banco La Nacion, and they will only open one type, a cuenta de ahorros.
No privately owned bank would let her open account.
But she went to the Banco La Nacion on Santa Fe near Plaza Italia, sat, as she calls it, "playing bingo" (waiting for her torno) for over an hour, and, at the end, she got a bank account.
We now have a tarjeta for the ATM, which will work to withdraw and deposit at any LINK ATM, we have Home Banking (online bill paying) and we have debito automatico for our utility bills, which was our main goal for doing this in the first place.
So it worked once. Which, of course, does not mean it will work again, but its worth a try.
We live mostly in the USA, and paying our bills online is a HUGE improvement for us over paying somebody to pay our bills in cash in Buenos Aires, and somehow getting them cash.
Of course, this bank account does not allow you to electronically transfer funds from outside the country- I dont think that is possible no matter what. We have to manually deposit pesos, not dollars, into our account, but we have various tricks for that. Friends are handy to have in BsAs.
When I first moved to LA, back in the 80's, a friend told me- first thing about Los Angeles, you gotta have a backup. For everything. Well, that goes double for Buenos Aires...