There’s Some Nuance, But in Effect.

It's true in some states but also not relevant in many ways. It was a largely cash based society. My grandmother had a bank account prior to WW2 as a young adult in Idaho. Usually the stores kept a leger or tab and you would come pay that off in person with cash in hand at the end of the month. Your bank wasn't needed unless you were getting a loan or had such large assets it would be dangerous to travel with it.