Personal Capital, for example, offers users with a net worth of $100,000 or more free financial advisory services, which could undercut paid services offered by banks.
Cliff Canan, founder and CEO of Nooch, a startup that allows users to electronically exchange money, said banks also are worried about maintaining customer loyalty.
"Banks are threatened because they have always 'owned' the customer," Canan said. "Everything in a person's financial life has always been run through a bank: credit cards, household bills, ATMs, paper checks, mortgages. ... So now new services that specialize in doing just one of those things really well are chipping away at every front. Even when the banks aren't losing revenue directly, they are losing 'touch' with a customer."
Another concern that may lead banks to limit access to some online financial services is that many free fin-tech services also present users with specific offers that are essentially advertisements for a rival bank.
"Banks want to control the interaction with their customers and don't want other companies to have access to sell competitors' products or harvest the customers' data," said Saunders, the National Consumer Law Center official.
Mint.com declined to comment on the limited access issue, but said in a statement that it stands by its commitment to uphold security measures. The company said it uses bank-level security to protect customer data, so if consumers feel banking online, they also can be comfortable using Mint.
"Delivering secure and seamless connectivity is a shared priority across Mint and thousands of our financial institution partners," said Mint representative Holly Perez. "We continuously work with them to ensure we deliver a great customer experience. This includes upholding our rigorous data stewardship and privacy policies."
Other sites say they, too, employ cutting-edge security measures to safeguard data.
Nooch, for example, says it uses government-grade data encryption.
Still, banks continue to express concern over aggregator site security. The Wall Street Journal reported in its story that J.P. Morgan's Chief Executive Jamie Dimon met last week with Consumer Financial Protection Bureau chief Richard Cordray to discuss the issues with aggregators.
It also reported that the Financial Services Information Sharing and Analysis Center is working to establish security guidelines for these services to follow. A spokesman for the group told NBC News that it is working with other industry groups to develop "information sharing best practices," not security guidelines specifically for third-party aggregators.
In any case, operators of some third-party personal finance sites say that banks should get their own houses in order in terms of security.
"There's a bit of irony here," said Joseph. "Banks are saying, 'you're not secure enough.' But banks have been involved in some pretty big security issues. And third party aggregators? They're tech firms. They haven't been breached. It could affect us, but I think we're all getting much smarter about security."