This is a pretty simplistic article.
first, everybody I know in Argentina uses their bank every day, and pay for everything from a coke at the kiosko to their utility bill by transfering money direct from their bank account.
So its not exactly they dont "trust" the bank.
Its that the peso is not safe against the constantly increasing value of the dollar. And that interest rates paid by banks on savings are not worth risking the loss of value against the dollar.
Since most imports, and most of argentinas exports, are priced in dollars, the FX issue is a giant part of what people call "inflation".
The US hundred dollar bill is the paper currency of choice in huge swaths of the globe- Argentina is not unique in this respect.
Approximately half of all US hundred dollar bills are outside of the US, being used for a stable currency. A lot of this is illegal business, or tax avoidance.
Which is another thing the article skips over- a lot of the cash use in Argentina is to avoid taxes.
In the US, the laws and banking system work much better to track untaxed transactions, and tax them- hence the lower use of cash.
The Argentine use of US cash is more a testimony to how bad the enforcement systems and laws are on things like property transactions.
Argentines risk trusting banks in the US and Uruguay, for example, even though there is risk of bank collapses in both countries.
Argentines often point to the coralito, in 2000, as a reason not to trust banks here, and to keep there money in Urugayan banks- but in 2002, the Urugayan bank crisis caused a huge run on the banks, and five major banks collapsed, and hundreds of millions of deposters money vanished- and yet, Argentines still "trust" Uruguayan banks, which really means, tax evasion.