Also, what could be called credit-union deserts. Lots of people don't have access to a credit union, and the large banks charge huge fees on poor people (see "the high cost of being poor"[0]). Past that, some of the above poor people have had terrible experiences with banks and want nothing to do with them. It easily adds up to that ~10% mentioned in the article.
[0] http://www.washingtonpost.com/wp-dyn/content/article/2009/05...
Some banks are doing these Pre-paid-ish cards now. I know Chase has Liquid, other banks may call it something else. For the most part, it functions mostly like a debit card backed by an actual checking account. But the requirements are far lower. They don't give a flying fuck who you are. You can even get checks to access the funds on the card.
And for like 90% of the time, you'll never realize you don't actually have a checking account. You won't realize that your money isn't technically backed by the bank. Then that 10% of the time will make your life inconvenient.
So I'd say that access to a card-based payment method doesn't seem insurmountable. But an actual checking account could still be out of the reach of some people.
The last checking account I opened just took $5 to open the account (technically a "membership" fee at a credit union). No any proof of employment, income, ar assets was needed [0], and I left with a debit card that day. Total time involvement was maybe 15 minutes.
[0] I just re-checked and all that is needed is SSN, Government ID, and the initial deposit (as low as $5, can be paid with cash, debit, credit, or check)