Most Americans distrust banks with their data

Implications of Lending Club CEO's resignation
Implications of Lending Club CEO's resignation

Most Americans don't trust anyone with their data — including Wall Street banks.

And how protective bank customers are over their data might provide some ideas to big banks about how to best keep them happy. Nearly 1 in 5 Americans (18 percent) said they would rather break a bone than have their payment information stolen; and 51 percent say there's no one they trust with their data.

The trends come from a joint Harris Poll/Feedzai study that sampled more than 2,000 U.S. adults and is called the Consumer Trust Survey. Just 1 in 4 respondents said they trusted banking sites the most with their information, according to the study released Thursday.

"There is still a long way to go to make people trust the firms they share their data with," said Nuno Sebastiao, CEO and co-founder of Feedzai.

Caspar Benson | Getty Images

Feedzai is a start-up providing fraud prevention services to payments firms.

There may be another culprit for Americans' frustration with banks and data protection.

The U.S. lags other developed nations, including Australia, the U.K. and Canada in smartphone access to mobile banking, according to a separate study, Adobe's State of Banking survey.

Read MoreThis issue is posing the biggest threat to online lending start-ups

And that's a potential headache for U.S. banks, which are closing branches and bolstering digital efforts to cater to new customers. The Adobe survey highlighted that 53 percent of millennials do more than half of their banking online; and that Gen Xers manage 62 percent of their banking mostly online.

"Most of the younger generation do not want to go into retail banks," said Tamara Gaffney, principal analyst and director at Adobe Systems.

But as the industry pushes from the desktop to the smartphone, banks' advantage with younger consumers could be threatened. The Adobe survey said 39 percent of millennials and 36 percent of Gen Xers expressed concern about the quality of mobile apps.