A person who owns a physical copy of a copyrighted work, which was obtained lawfully, need not surrender the physical copy (or the artifact containing the copy) to the copyright-holder. I own many books, but I would not be required to give them up to the authors should the authors demand them.
If the data was provided under a NDA, or some other valid contract limiting access, then the other party can insist on that contract being honored. If that contract provides for deletion of the content on demand, or after a specified time, then those contract provisions must be honored or a suit for breach of contract would have merit. Exactly what would follow would depend on the specific wording of the contract, and to some extent on the jurisdiction where all this took place.
If there was no contract, and the copy of the content was given to the owner of the hard drive with the permission of the copyright-holder, or the holder's authorized agent, then the holder has no recourse as long as the hard drive is not used to make additional copies or otherwiuse infringe the copyright.
In a significant sense, ownership of the storage medium does trump "ownership" of the content. We often speak of someone "owning" a document, but what is really owned is the copyright on that document. That gives the copyright holder a number of rights, but not the right to control what the owner of a physical copy does with it as long as that owner does not make unauthorized copies, or violate any of the other exclusive rights that are part of copyright. Nor does the copyright-holder have the right to control who reads a lawful copy, as long as additional copies are not made. In the US the possessor of a copy will have additional rights under the "fair use' doctrine.
Moving a document to a different storage medium would involve making a copy. This would be copyright infringement unless permission had been granted, or it was permitted as fair use (in the US). Note that making a backup of a computer program or an electronic document is normally considered to be fair use. Note also that the only way in which this could be enforced would be through a lawsuit for copyright infringement, requesting an injunction from the court. If the document has little economic value, such a suit might not be successful. In any case bringing it would involve some costs, and would (in the US) require registration of the copyright before suit could be filed.