A) A credit account is not the same thing as a checking account or credit union account
B) Plenty of people, even in the US, operate without any of these things. It's not fun, but it's absolutely possible.
After my company crashed, my wife divorced me and then I got cancer -- things were pretty grim on my credit-worthiness story. Net-net: I went without a bank-account for a few years and learned to live with pre-paid phones, money-orders, cashing checks at pawn-shops and pre-paid debit cards, and (for medical and other reasons - not able to drive. Good news: I saved on car insurance, gas and parking). All-in-all ... not a lot of fun (it's very expensive and time-consuming to be poor in America!).
But! As you say: it is do-able.