This is a hole in the Constitution that would be better patched, at least with statute, better with an amendment. The fourth amendment says

  The right of the people to be secure in their persons, houses, papers, and effects...

Who is "their" here? In terms of property rights it's the people who own those digital "papers". The individuals who that data is about do no maintain or control that data, and could not destroy it, meaning they do not functionally have property rights over it. If I write in my notebook that you have blonde hair, the notebook is still my property. There isn't anything I could write about you in it that would make it yours (other than maybe "I hereby give this notebook to Joe Bloe").

Attempts to interpret the Constitution otherwise are, IMHO, attempts at good policy, but unstable as law. So we should fix it either by giving people property rights to that data (so that they can destroy or change it without permission) or to explicitly require warrants for access to PII owned by third parties.