While it's up to the consumer to share the data in the first place, they may have no say over how the information is used after they hand it over. Privacy advocates worry that people will provide sensitive medical information that they don't realize might be re-sold or re-shared to other entities.

Administration officials insist that the rules will demand tech companies to be upfront with consumers about how their data will be used. But these assurances are hardly enough for some. Critics worry this is one step closer to giving the major titans of data –– Facebook, Google and Amazon –– more ways to monitor the lives of their customers.

"This is not about interoperability — this is about having access to data," said Jeff Chester, head of the Center for Digital Democracy. "The health data is going to give them insights into many other aspects of your life."

At least one major tech firm, however, is adamantly opposed to the proposal: Epic Systems, a privately-held company based outside of Madison, Wisconsin that is the largest provider of software for electronic health care records.

Epic has begun funding ads in the Washington D.C. Metro opposing the proposal, warning of dangers to patient privacy. Sixty health systems joined it in signing a letter telling the Department of Health and Human Services to reconsider the proposal.

However, the fact that more hospitals didn't sign the letter suggests that some providers perceive an advantage in allowing health apps greater access to patient data.

"Their absence represents a thundering silence," David Brailer, who served as National Health Information Technology Coordinator under President George W. Bush, tells CNBC. "Many health systems are quietly discussing how the data access and data fluidity actually benefits them in the long-run."

Read more: 

• Managing medical records via smartphone might take a while to catch on
• Digging deeper: Health data mining platforms surge ahead
• Interoperability may jeopardize consumers' health care privacy