That's a fair criticism. The Bankrate report was marketing material, based on a survey, and someone's answer would depend on what they considered a "savings account" to be. I don't have a savings account with my bank because, as you say, it's not worth it. I do have a small amount of savings in an investment account. Whether I'd consider that when asked about a savings account or not, I dunno.

However, the Fed has asked a different question intended to drill down into the same problem, and found that 47% of people responding would pay for a $400 emergency by borrowing money or selling something (https://www.theatlantic.com/magazine/archive/2016/05/my-secr..., also cites Bankrate though).

I'm unaware though of any studies finding that the majority of Americans have a significant amount of money (let's say a thousand or more) in a liquid asset of some kind. If you know of any, that would be some welcomed good news.